A Statistical Scheme for the Seasonal Forecasting of North China's Surface Air Temperature duri

SEASONAL ENERGY EFFICIENCY RATIOOn January 1, 1979, Carrier Corporation started expressing its residential cooling unit and heat pump efficiencies in Seasonal Energy Efficiency Ratios (SEER).EER - By way of background: ARI introduced the Energy Efficiency Ratio (EER) in 1975. This was an HVAC industry instituted and policed way to determine the relative efficiencies of one unit to another in the cooling mode. EER was determined by dividing the published steady state capacity by the published steady sate power input at 80°F dB/ 67°F Wb indoor and 95°F dB outdoor. This was quite objective yet unrealistic with respect to system "real world"operating conditions.1) Congress passed public Law No. 94-163 whereby labeling of certain appliances(including 1-phase air conditioners through 65,000 Btuh capacity) was mandated.2) The National Bureau of Standards (among others) was commissioned to develop testingstandards for air conditioners that would fairly and accurately determine the values thatwould show on such a label. Such information would include the unit's capacity, theseasonal energy efficiency ratio (SEER), and the estimated yearly cost of operation underspecific stated conditions.3) The Federal Trade Commission was given the task of coming up with the specific formatfor the label.4) Testing on the product is required such that there is 90% (or better) statistical confidencethat the product's energy usage is within 5% of the advertised values, including that shownon the label.5) These new laws affect only units with an ARI capacity of 65,000 Btuh or less, includingYAC's, PAC's, Heat Pumps, and Split Systems. There are laws governing RAC's, butthey are not covered in this write-up.SEER - The new concept of Seasonal Energy Efficiency Ratio (SEER) is an improvement over the old EER concept in two very important ways and is intended to better approximate what happens in the actual end use application for the product. Instead of a single test as is used in determining EER in the old concept, the new SEER concept requires four tests to take into consideration a variation in outdoor temperature as well as the effect of cycling the unit on and off.The SEER of a system is determined by multiplying the steady state energy efficiency ratio (EER) measured at conditions of 82°F outdoor temperature, 80°F dB/ 67°F wb indoor entering air temperature by the Part Load Factor (PLF) of the system.(PLF is supplied by the government.)Heating Seasonal Performance Factor (HSPF)HSPF =The total watt-hours input during the entire heating season are used to calculate the HSPF.By definition - For electric resistance heaters:HSPF = 1.0If heat pump HSPF is greater than 1.0, then heat pump is more efficient than resistance heat.For example:If HSPF = 1.83Heat Pump is 83% more efficient than resistance heat on a seasonal basis.COEFFICIENT OF PERFORMANCE (COP)COP is the ratio of work output divided by work input. The output is the amount of heat absorbed by the system. The input is the amount of energy required to produce this output. However, in a heat pump system, the output is the heat of rejection of the total system. The energy input is inclusive of compressor, indoor, and outdoor fan motor watts.COP =Btuh Input = Total watts input (compressor, indoor, andoutdoor fan motor) x 3.4141 Watt/Hr = 3.414 Btuh1 kw/hr = 3414 BtuhBtuh Output = Rated output from product sheetEFFICIENCY RATINGS -- WHAT SEER MEANS TO YOUThe purpose of rating the efficiency of an air conditioner is to indicate the relative amount of energy needed to provide a specific cooling output. The more efficient the equipment, the less energy will be used to do the same job.It's a lot like the miles per gallon ratings for automobiles. However, instead of "MPG", central residential air conditioners now use the designation "SEER" which stands for Seasonal Energy Efficiency Ratio.Previously, the air conditioning industry used the term "EER", which stood for Energy Efficiency Ratio. This was a simple mathematical ratio of cooling output measured in British Thermal Units per Hour (BTUH) versus electrical power input (watts). Recently, the U.S. Department of Energy (DOE) developed a more complicated test method, which rates the performance of a unit over a wide range of operating conditions. The result (SEER) in indicative of the unit's operation throughout the cooling season.Assume a home requires a unit with a cooling capacity of 36,000 BTUH and is located where the cooling system necessitates running the unit a total of 1,500 hours. Assume electricity costs residential customers 5 cents per kilowatt-hour.FORMULA -- APPROXIMATE YEARLY COST OF OPERATIONCAPACITY (BTUH) X COOLING LOAD HOURS X ELECTRIC RATE = COST OF OPERATION SEER 1,000In the case of our hypothetical house, the formula would go like this:SEER 6.0: 36,000 X1,500 X .05 = $450.6.0 1,000SEER 8.0: 36,000 X1,500 X .05 = $290.9.3 1,000From this, you can see that the higher efficiency unit would save $160. each cooling season. Obviously, this amount will vary in real-life situations depending on:1. Whether the unit operates more or less than the 1,500 hours used in the example,2. Family size and living habits, and3. The electric rates.(Your local electric utility should be able to provide information on cooling load hours for yourarea as well as electricity rates.)Nevertheless, the example does illustrate that higher efficiency results in lower energy costs. However, since the higher efficiency model is often more expensive, you may want to calculate the payback period in which it will "pay for itself" in terms of lower utility bills.The SEER of a system is determined by multiplying the steady state Energy Efficiency Ratio (EER) measured at conditions of 82°F outdoor temperature, 80°F dB/ 67°F Wb indoor entering air temperature by the Part Load Factor (PLF) of the system. That is:SEER = PLF X EER82FThe PLF is a measure of the cyclic performance (CD) of a system and is calculated as follows:PLF = 1 - (CD X 0.5)The CD value in the above equation has been determined by the government to be 0.25. Hence, the government contends that the PLF should equal:[1 - (.25 x .5)] which yields:PLF = 0.875A number of major HVAC manufacturers have argued that the "CD = 0.25" criterion is too severe and not representative of modern cooling units. As a consequence, the government has established a procedure by which each manufacture may calculate their actual CD factor. This calculation involves making two additional tests on a cooling system with an outdoor entering air condition of 80°F dB/ 57°F Wb (dry coil test). One test (Test A) requires the system to be cycled on for 6 minutes and off for 24 minutes to measure the cyclic response of the system. The second test (Test B) requires the unit to be run at a steady state (on all the time) and provides a basis for comparison with the cycling test. Data taken from the two tests is used to compute the CD factors as follows:1 -CD =Where: EER = capacity / wattsX 2.0CLF is an approximate of equipment run time.A CLF of .2, for instance, is equivalent to saying the unit will be running 20% of the time.。

CHAPTER 13FORECASTINGReview Questions13.1-1 Substantially underestimating demand is likely to lead to many lost sales, unhappycustomers, and perhaps allowing the competition to gain the upper hand in the marketplace. Significantly overestimating the demand is very costly due to excessive inventory costs, forced price reductions, unneeded production or storage capacity, and lost opportunity to market more profitable goods.13.1-2 A forecast of the demand for spare parts is needed to provide good maintenanceservice.13.1-3 In cases where the yield of a production process is less than 100%, it is useful toforecast the production yield in order to determine an appropriate value of reject allowance and, consequently, the appropriate size of the production run.13.1-4 Statistical models to forecast economic trends are commonly called econometricmodels.13.1-5 Providing too few agents leads to unhappy customers, lost calls, and perhaps lostbusiness. Too many agents cause excessive personnel costs.13.2-1 The company mails catalogs to its customers and prospective customers severaltimes per year, as well as publishing mini-catalogs in computer magazines. They then take orders for products over the phone at the company’s call center.13.2-2 Customers who receive a busy signal or are on hold too long may not call back andbusiness may be lost. If too many agents are on duty there may be idle time, which wastes money because of labor costs.13.2-3 The manager of the call center is Lydia Weigelt. Her current major frustration is thateach time she has used her procedure for setting staffing levels for the upcoming quarter, based on her forecast of the call volume, the forecast usually has turned out to be considerably off.13.2-4 Assume that each quarter’s cal l volume will be the same as for the preceding quarter,except for adding 25% for quarter 4.13.2-5 The average forecasting error is commonly called MAD, which stands for MeanAbsolute Deviation. Its formula is MAD = (Sum of forecasting errors) / (Number of forecasts)13.2-6 MSE is the mean square error. Its formula is (Sum of square of forecasting errors) /(Number of forecasts).13.2-7 A time series is a series of observations over time of some quantity of interest.13.3-1 In general, the seasonal factor for any period of a year measures how that periodcompares to the overall average for an entire year.13.3-2 Seasonally adjusted call volume = (Actual call volume) / (Seasonal factor).13.3-3 Actual forecast = (Seasonal factor)(Seasonally adjusted forecast)13.3-4 The last-value forecasting method sometimes is called the naive method becausestatisticians consider it naive to use just a sample size of one when additional relevant data are available.13.3-5 Conditions affecting the CCW call volume were changing significantly over the pastthree years.13.3-6 Rather than using old data that may no longer be relevant, this method averages thedata for only the most recent periods.13.3-7 This method modifies the moving-average method by placing the greatest weighton the last value in the time series and then progressively smaller weights on the older values.13.3-8 A small value is appropriate if conditions are remaining relatively stable. A largervalue is needed if significant changes in the conditions are occurring relatively frequently.13.3-9 Forecast = α(Last Value) + (1 –α)(Last forecast). Estimated trend is added to thisformula when using exponential smoothing with trend.13.3-10 T he one big factor that drives total sales up or down is whether there are any hotnew products being offered.13.4-1 CB Predictor uses the raw data to provide the best fit for all these inputs as well asthe forecasts.13.4-2 Each piece of data should have only a 5% chance of falling below the lower line and a5% chance of rising above the upper line.13.5-1 The next value that will occur in a time series is a random variable.13.5-2 The goal of time series forecasting methods is to estimate the mean of theunderlying probability distribution of the next value of the time series as closely as possible.13.5-3 No, the probability distribution is not the same for every quarter.13.5-4 Each of the forecasting methods, except for the last-value method, placed at leastsome weight on the observations from Year 1 to estimate the mean for each quarter in Year 2. These observations, however, provide a poor basis for estimating the mean of the Year 2 distribution.13.5-5 A time series is said to be stable if its underlying probability distribution usuallyremains the same from one time period to the next. A time series is unstable if both frequent and sizable shifts in the distribution tend to occur.13.5-6 Since sales drive call volume, the forecasting process should begin by forecastingsales.13.5-7 The major components are the relatively stable market base of numerous small-niche products and each of a few major new products.13.6-1 Causal forecasting obtains a forecast of the quantity of interest by relating it directlyto one or more other quantities that drive the quantity of interest.13.6-2 The dependent variable is call volume and the independent variable is sales.13.6-3 When doing causal forecasting with a single independent variable, linear regressioninvolves approximating the relationship between the dependent variable and the independent variable by a straight line.13.6-4 In general, the equation for the linear regression line has the form y = a + bx. Ifthere is more than one independent variable, then this regression equation has a term, a constant times the variable, added on the right-hand side for each of these variables.13.6-5 The procedure used to obtain a and b is called the method of least squares.13.6-6 The new procedure gives a MAD value of only 120 compared with the old MADvalue of 400 with the 25% rule.13.7-1 Statistical forecasting methods cannot be used if no data are available, or if the dataare not representative of current conditions.13.7-2 Even when good data are available, some managers prefer a judgmental methodinstead of a formal statistical method. In many other cases, a combination of the two may be used.13.7-3 The jury of executive opinion method involves a small group of high-level managerswho pool their best judgment to collectively make a forecast rather than just the opinion of a single manager.13.7-4 The sales force composite method begins with each salesperson providing anestimate of what sales will be in his or her region.13.7-5 A consumer market survey is helpful for designing new products and then indeveloping the initial forecasts of their sales. It is also helpful for planning a marketing campaign.13.7-6 The Delphi method normally is used only at the highest levels of a corporation orgovernment to develop long-range forecasts of broad trends.13.8-1 Generally speaking, judgmental forecasting methods are somewhat more widelyused than statistical methods.13.8-2 Among the judgmental methods, the most popular is a jury of executive opinion.Manager’s opinion is a close second.13.8-3 The survey indicates that the moving-average method and linear regression are themost widely used statistical forecasting methods.Problems13.1 a) Forecast = last value = 39b) Forecast = average of all data to date = (5 + 17 + 29 + 41 + 39) / 5 = 131 / 5 =26c) Forecast = average of last 3 values = (29 + 41 + 39) / 3 = 109 / 3 = 36d) It appears as if demand is rising so the average forecasting method seemsinappropriate because it uses older, out-of-date data.13.2 a) Forecast = last value = 13b) Forecast = average of all data to date = (15 + 18 + 12 + 17 + 13) / 5 = 75 / 5 =15c) Forecast = average of last 3 values = (12 + 17 + 13) / 3 = 42 / 3 = 14d) The averaging method seems best since all five months of data are relevant indetermining the forecast of sales for next month and the data appears relativelystable.13.3MAD = (Sum of forecasting errors) / (Number of forecasts) = (18 + 15 + 8 + 19) / 4 = 60 / 4 = 15 MSE = (Sum of squares of forecasting errors) / (Number of forecasts) = (182 + 152 + 82 + 192) / 4 = 974 / 4 = 243.513.4 a) Method 1 MAD = (258 + 499 + 560 + 809 + 609) / 5 = 2,735 / 5 = 547Method 2 MAD = (374 + 471 + 293 + 906 + 396) / 5 = 2,440 / 5 = 488Method 1 MSE = (2582 + 4992 + 5602 + 8092 + 6092) / 5 = 1,654,527 / 5 = 330,905Method 2 MSE = (3742 + 4712 + 2932 + 9062 + 3962) / 5 = 1,425,218 / 5 = 285,044Method 2 gives a lower MAD and MSE.b) She can use the older data to calculate more forecasting errors and compareMAD for a longer time span. She can also use the older data to forecast theprevious five months to see how the methods compare. This may make her feelmore comfortable with her decision.13.5 a)b)c)d)13.6 a)b)This progression indicatesthat the state’s economy is improving with the unemployment rate decreasing from 8% to 7% (seasonally adjusted) over the four quarters.13.7 a)b) Seasonally adjusted value for Y3(Q4)=28/1.04=27,Actual forecast for Y4(Q1) = (27)(0.84) = 23.c) Y4(Q1) = 23 as shown in partb Seasonally adjusted value for Y4(Q1) = 23 / 0.84 = 27 Actual forecast for Y4(Q2) = (27)(0.92) = 25Seasonally adjusted value for Y4(Q2) = 25 / 0.92 = 27 Actual forecast for Y4(Q3) = (27)(1.20) = 33Seasonally adjusted value for Y4(Q3) = 33/1.20 = 27Actual forecast for Y4(Q4) = (27)(1.04) = 28d)13.8 Forecast = 2,083 – (1,945 / 4) + (1,977 / 4) = 2,09113.9 Forecast = 782 – (805 / 3) + (793 / 3) = 77813.10 Forecast = 1,551 – (1,632 / 10) + (1,532 / 10) = 1,54113.11 Forecast(α) = α(last value) + (1 –α)(last forecast)Forecast(0.1) = (0.1)(792) + (1 –0.1)(782) = 783 Forecast(0.3) = (0.3)(792) + (1 –0.3)(782) = 785 Forecast(0.5) = (0.5)(792) + (1 – 0.5)(782) = 78713.12 Forecast(α) = α(last value) + (1 –α)(last forecast)Forecast(0.1) = (0.1)(1,973) + (1 –0.1)(2,083) = 2,072 Forecast(0.3) = (0.3)(1,973) + (1 –0.3)(2,083) = 2,050 Forecast(0.5) = (0.5)(1,973) + (1 – 0.5)(2,083) = 2,02813.13 a) Forecast(year 1) = initial estimate = 5000Forecast(year 2) = α(last value) + (1 –α)(last forecast)= (0.25)(4,600) + (1 –0.25)(5,000) = 4,900 Forecast(year 3) = (0.25)(5,300) + (1 – 0.25)(4,900) = 5,000b) MAD = (400 + 400 + 1,000) / 3 = 600MSE = (4002 + 4002 + 1,0002) / 3 = 440,000c) Forecast(next year) = (0.25)(6,000) + (1 – 0.25)(5,000) = 5,25013.14 Forecast = α(last value) + (1 –α)(last forecast) + Estimated trendEstimated trend = β(Latest trend) + (1 –β)(Latest estimate of trend) Latest trend = α(Last value – Next-to-last value) + (1 –α)(Last forecast – Next-to-last forecast)Forecast(year 1) = Initial average + Initial trend = 3,900 + 700 = 4,600Forecast (year 2) = (0.25)(4,600) + (1 –0.25)(4,600)+(0.25)[(0.25)(4,600 –3900) + (1 –0.25)(4,600 –3,900)] + (1 –0.25)(700) = 5,300Forecast (year 3) = (0.25)(5,300) + (1 – 0.25)(5,300) + (0.25)[(0.25)(5,300 – 4,600) + (1 – 0.25)(5,300 – 4,600)]+(1 – 0.25)(700) = 6,00013.15 Forecast = α(last value) + (1 –α)(last forecast) + Estimated trendEstimated trend = β(Latest trend) + (1 –β)(Latest estimate of trend) Latest trend = α(Last value – Next-to-last value) + (1 –α)(Last forecast – Next-to-last forecast)Forecast = (0.2)(550) + (1 – 0.2)(540) + (0.3)[(0.2)(550 – 535) + (1 – 0.2)(540 –530)] + (1 – 0.3)(10) = 55213.16 Forecast = α(last value) + (1 –α)(last forecast) + Estimated trendEstimated trend = β(Latest trend) + (1 –β)(Latest estimate of trend) Latest trend = α(Last value – Next-to-last value) + (1 –α)(Last forecast – Next-to-last forecast)Forecast = (0.1)(4,935) + (1 – 0.1)(4,975) + (0.2)[(0.1)(4,935 – 4,655) + (1 – 0.1) (4,975 – 4720)] + (1 – 0.2)(240) = 5,21513.17 a) Since sales are relatively stable, the averaging method would be appropriate forforecasting future sales. This method uses a larger sample size than the last-valuemethod, which should make it more accurate and since the older data is stillrelevant, it should not be excluded, as would be the case in the moving-averagemethod.b)c)d)e) Considering the MAD values (5.2, 3.0, and 3.9, respectively), the averagingmethod is the best one to use.f) Considering the MSE values (30.6, 11.1, and 17.4, respectively), the averagingmethod is the best one to use.g) Unless there is reason to believe that sales will not continue to be relatively stable,the averaging method should be the most accurate in the future as well.13.18 Using the template for exponential smoothing, with an initial estimate of 24, thefollowing forecast errors were obtained for various values of the smoothing constant α:use.13.19 a) Answers will vary. Averaging or Moving Average appear to do a better job thanLast Value.b) For Last Value, a change in April will only affect the May forecast.For Averaging, a change in April will affect all forecasts after April.For Moving Average, a change in April will affect the May, June, and July forecast.c) Answers will vary. Averaging or Moving Average appear to do a slightly better jobthan Last Value.d) Answers will vary. Averaging or Moving Average appear to do a slightly better jobthan Last Value.13.20 a) Since the sales level is shifting significantly from month to month, and there is noconsistent trend, the last-value method seems like it will perform well. Theaveraging method will not do as well because it places too much weight on olddata. The moving-average method will be better than the averaging method butwill lag any short-term trends. The exponential smoothing method will also lagtrends by placing too much weight on old data. Exponential smoothing withtrend will likely not do well because the trend is not consistent.b)Comparing MAD values (5.3, 10.0, and 8.1, respectively), the last-value method is the best to use of these three options.Comparing MSE values (36.2, 131.4, and 84.3, respectively), the last-value method is the best to use of these three options.c) Using the template for exponential smoothing, with an initial estimate of 120, thefollowing forecast errors were obtained for various values of the smoothingconstant α:constant is appropriate.d) Using the template for exponential smoothing with trend, using initial estimates of120 for the average value and 10 for the trend, the following forecast errors wereobtained for various values of the smoothing constants α and β:constants is appropriate.e) Management should use the last-value method to forecast sales. Using thismethod the forecast for January of the new year will be 166. Exponentialsmoothing with trend with high smoothing constants (e.g., α = 0.5 and β = 0.5)also works well. With this method, the forecast for January of the new year will be165.13.21 a) Shift in total sales may be due to the release of new products on top of a stableproduct base, as was seen in the CCW case study.b) Forecasting might be improved by breaking down total sales into stable and newproducts. Exponential smoothing with a relatively small smoothing constant canbe used for the stable product base. Exponential smoothing with trend, with arelatively large smoothing constant, can be used for forecasting sales of each newproduct.c) Managerial judgment is needed to provide the initial estimate of anticipated salesin the first month for new products. In addition, a manger should check theexponential smoothing forecasts and make any adjustments that may benecessary based on knowledge of the marketplace.13.22 a) Answers will vary. Last value seems to do the best, with exponential smoothingwith trend a close second.b) For last value, a change in April will only affect the May forecast.For averaging, a change in April will affect all forecasts after April.For moving average, a change in April will affect the May, June, and July forecast.For exponential smoothing, a change in April will affect all forecasts after April.For exponential smoothing with trend, a change in April will affect all forecastsafter April.c) Answers will vary. last value or exponential smoothing seem to do better than theaveraging or moving average.d) Answers will vary. last value or exponential smoothing seem to do better than theaveraging or moving average.13.23 a) Using the template for exponential smoothing, with an initial estimate of 50, thefollowing MAD values were obtained for various values of the smoothing constantα:Choose αb) Using the template for exponential smoothing, with an initial estimate of 50, thefollowing MAD values were obtained for various values of the smoothing constantα:Choose αc) Using the template for exponential smoothing, with an initial estimate of 50, thefollowing MAD values were obtained for various values of the smoothing constantα:13.24 a)b)Forecast = 51.c) Forecast = 54.13.25 a) Using the template for exponential smoothing with trend, with an initial estimatesof 50 for the average and 2 for the trend and α = 0.2, the following MAD values were obtained for various values of the smoothing constant β:Choose β = 0.1b) Using the template for exponential smoothing with trend, with an initial estimatesof 50 for the average and 2 for the trend and α = 0.2, the following MAD valueswere obtained for various values of the smoothing constant β:Choose β = 0.1c) Using the template for exponential smoothing with trend, with an initial estimatesof 50 for the average and 2 for the trend and α = 0.2, the following MAD valueswere obtained for various values of the smoothing constant β:13.26 a)b)0.582. Forecast = 74.c) = 0.999. Forecast = 79.13.27 a) The time series is not stable enough for the moving-average method. Thereappears to be an upward trend.b)c)d)e) Based on the MAD and MSE values, exponential smoothing with trend should beused in the future.β = 0.999.f)For exponential smoothing, the forecasts typically lie below the demands.For exponential smoothing with trend, the forecasts are at about the same level as demand (perhaps slightly above).This would indicate that exponential smoothing with trend is the best method to usehereafter.13.2913.30 a)factors:b)c) Winter = (49)(0.550) = 27Spring = (49)(1.027) = 50Summer = (49)(1.519) = 74Fall = (49)(0.904) = 44d)e)f)g) The exponential smoothing method results in the lowest MAD value (1.42) and thelowest MSE value (2.75).13.31 a)b)c)d)e)f)g) The last-value method with seasonality has the lowest MAD and MSE value. Usingthis method, the forecast for Q1 is 23 houses.h) Forecast(Q2) = (27)(0.92) = 25Forecast(Q3) = (27)(1.2) = 32Forecast(Q4) = (27)(1.04) = 2813.32 a)b) The moving-average method with seasonality has the lowest MAD value. Using13.33 a)b)c)d) Exponential smoothing with trend should be used.e) The best values for the smoothing constants are α = 0.3, β = 0.3, and γ = 0.001.C28:C38 below.13.34 a)b)c)d)e) Moving average results in the best MAD value (13.30) and the best MSE value(249.09).f)MAD = 14.17g) Moving average performed better than the average of all three so it should beused next year.h) The best method is exponential smoothing with seasonality and trend, using13.35 a)••••••••••0100200300400500600012345678910S a l e sMonthb)c)••••••••••0100200300400500600012345678910S a l e sMonthd) y = 410.33 + (17.63)(11) = 604 e) y = 410.33 + (17.63)(20) = 763f) The average growth in sales per month is 17.63.13.36 a)•••01000200030004000500060000123A p p l i c a t i o n sYearb)•••01000200030004000500060000123A p p l i c a t i o n sYearc)d) y (year 4) = 3,900+ (700)(4) = 6,700 y (year 5) = 3,900 + (700)(5) = 7,400 y (year 6) = 3,900 + (700)(6) = 8,100 y (year 7) = 3,900 + (700)(7) =8,800y (year 8) = 3,900 + (700)(8) = 9,500e) It does not make sense to use the forecast obtained earlier of 9,500. Therelationship between the variable has changed and, thus, the linear regression that was used is no longer appropriate.f)•••••••0100020003000400050006000700001234567A p p l i c a t i o n sYeary =5,229 +92.9x y =5,229+(92.9)(8)=5,971the forecast that it provides for year 8 is not likely to be accurate. It does not make sense to continue to use a linear regression line when changing conditions cause a large shift in the underlying trend in the data.g)Causal forecasting takes all the data into account, even the data from before changing conditions cause a shift. Exponential smoothing with trend adjusts to shifts in the underlying trend by placing more emphasis on the recent data.13.37 a)••••••••••50100150200250300350400450500012345678910A n n u a l D e m a n dYearb)c)••••••••••50100150200250300350400450500012345678910A n n u a l D e m a n dYeard) y = 380 + (8.15)(11) = 470 e) y = 380 = (8.15)(15) = 503f) The average growth per year is 8.15 tons.13.38 a) The amount of advertising is the independent variable and sales is the dependentvariable.b)•••••0510*******100200300400500S a l e s (t h o u s a n d s o f p a s s e n g e r s )Amount of Advertising ($1,000s)c)•••••0510*******100200300400500S a l e s (t h o u s a n d s o f p a s s e n g e r s )Amount of Advertising ($1,000s)d) y = 8.71 + (0.031)(300) = 18,000 passengers e) 22 = 8.71 + (0.031)(x ) x = $429,000f) An increase of 31 passengers can be attained.13.39 a) If the sales change from 16 to 19 when the amount of advertising is 225, then thelinear regression line shifts below this point (the line actually shifts up, but not as much as the data point has shifted up).b) If the sales change from 23 to 26 when the amount of advertising is 450, then the linear regression line shifts below this point (the line actually shifts up, but not as much as the data point has shifted up).c) If the sales change from 20 to 23 when the amount of advertising is 350, then the linear regression line shifts below this point (the line actually shifts up, but not as much as the data point has shifted up).13.40 a) The number of flying hours is the independent variable and the number of wingflaps needed is the dependent variable.b)••••••024*********100200W i n g F l a p s N e e d e dFlying Hours (thousands)c)d)••••••024*********100200W i n g F l a p s N e e d e dFlying Hours (thousands)e) y = -3.38 + (0.093)(150) = 11f) y = -3.38 + (0.093)(200) = 1513.41 Joe should use the linear regression line y = –9.95 + 0.10x to develop a forecast forCase13.1 a) We need to forecast the call volume for each day separately.1) To obtain the seasonally adjusted call volume for the past 13 weeks, we firsthave to determine the seasonal factors. Because call volumes follow seasonalpatterns within the week, we have to calculate a seasonal factor for Monday,Tuesday, Wednesday, Thursday, and Friday. We use the Template for SeasonalFactors. The 0 values for holidays should not factor into the average. Leaving themblank (rather than 0) accomplishes this. (A blank value does not factor into theAVERAGE function in Excel that is used to calculate the seasonal values.) Using thistemplate (shown on the following page, the seasonal factors for Monday, Tuesday,Wednesday, Thursday, and Friday are 1.238, 1.131, 0.999, 0.850, and 0.762,respectively.2) To forecast the call volume for the next week using the last-value forecasting method, we need to use the Last Value with Seasonality template. To forecast the next week, we need only start with the last Friday value since the Last Value method only looks at the previous day.The forecasted call volume for the next week is 5,045 calls: 1,254 calls are received on Monday, 1,148 calls are received on Tuesday, 1,012 calls are received on Wednesday, 860 calls are received on Thursday, and 771 calls are received on Friday.3) To forecast the call volume for the next week using the averaging forecasting method, we need to use the Averaging with Seasonality template.The forecasted call volume for the next week is 4,712 calls: 1,171 calls are received on Monday, 1,071 calls are received on Tuesday, 945 calls are received on Wednesday, 804 calls are received on Thursday, and 721 calls are received onFriday.4) To forecast the call volume for the next week using the moving-average forecasting method, we need to use the Moving Averaging with Seasonality template. Since only the past 5 days are used in the forecast, we start with Monday of the last week to forecast through Friday of the next week.The forecasted call volume for the next week is 4,124 calls: 985 calls are received on Monday, 914 calls are received on Tuesday, 835 calls are received on Wednesday, 732 calls are received on Thursday, and 658 calls are received on Friday.5) To forecast the call volume for the next week using the exponential smoothing forecasting method, we need to use the Exponential with Seasonality template. We start with the initial estimate of 1,125 calls (the average number of calls on non-holidays during the previous 13 weeks).The forecasted call volume for the next week is 4,322 calls: 1,074 calls are received on Monday, 982 calls are received on Tuesday, 867 calls are received onWednesday, 737 calls are received on Thursday, and 661 calls are received on Friday.b) To obtain the mean absolute deviation for each forecasting method, we simplyneed to subtract the true call volume from the forecasted call volume for each day in the sixth week. We then need to take the absolute value of the five differences.Finally, we need to take the average of these five absolute values to obtain the mean absolute deviation.1) The spreadsheet for the calculation of the mean absolute deviation for the last-value forecasting method follows.This method is the least effective of the four methods because this method depends heavily upon the average seasonality factors. If the average seasonality factors are not the true seasonality factors for week 6, a large error will appear because the average seasonality factors are used to transform the Friday call volume in week 5 to forecasts for all call volumes in week 6. We calculated in part(a) that the call volume for Friday is 0.762 times lower than the overall average callvolume. In week 6, however, the call volume for Friday is only 0.83 times lower than the average call volume over the week. Also, we calculated that the call volume for Monday is 1.34 times higher than the overall average call volume. In Week 6, however, the call volume for Monday is only 1.21 times higher than the average call volume over the week. These differences introduce a large error.。

“工程地质”主要术语（词汇）及用法slope failure,rockfall, ,landslide等★landslide area e.g. We cannot be certain whether landslides did or did not occur in the regions outside of the mapped landslide area.★landslide dam★landslide distribution e.g. Empirical studies suggest that the bedrock lithology, slope, seismic intensity, topographical amplification of ground motion, fracture systems in the underlying bedrock, groundwater conditions, and also the distribution of pre existing landslides all have some impact on the landslide distribution, among factors.★landslide hazard modeling e.g. The main objective of landslide hazard modeling is to predict areas prone to landslides either spatially or temporally.★landslide inventories e.g. In order to apply this approach to a global data set, we use multiple landslide inventories to calibrate the model. Using the model formula previously determined (using the Wenchuan earthquake data), we use the four datasets discussed in Section 1.3.1 in our global database to determine the coefficients for the global model.★landslide probability model e.g. The resulting database is used to build a predicative model of the probability of landslide occurrence.★landslide susceptibility★landslide observation e.g. Cells are classified as landslides if any portion of that grid cell contains a landslide observation, in order to easily incorporate binary observations into the logistic regression.★landslides e.g. Substantial effort has been invested to understand where seismically inducedlandslides may occur in the future, as they are a costly and frequently fatal threat in mountainous regions; Performance of the regression model is assessed using statistical goodness-of-fit metrics and a qualitative review to determine which combination of the proxies provides both the optimum predication of landslide-affected areas and minimizes the false alarms in non-landslide zones; Approximately 5% of all earthquake-related fatalities are caused by seismically induced landslides, in some cases causing a majority of non-shaking deaths; Possible case histories of earthquake-triggered landslides to add to the global dataset include….★landslip★limit equilibrium methods★line slope profile★linearly e.g. In order to determine if such an increase in water levels could be the cause of increased down slope movement the bottom head boundary condition of both the Shetran and Flac-tp model was increased linearly by 0 to 4 m over the length of the lower slope and linearly by 4 to 5 m over the length of the upper slope.★low angle failure★lower slope★macroscopic indicators e.g. Unsaturated residual shear strength can also be used as a macroscopic indicator of the nature of micro-structural changes experienced by the soils when subjected to drying.★material parameters★mechanical analysis★mechanical landslide modeling e.g. These data were originally calculated for the purpose of mechanical landslide modeling, and are used here as a statistical constraint on landslide susceptibility.★mechanical parameters★mechanical propertied★mechanical response★mechanical strains★mechanism e.g. The output pore water pressure were coupled to a mechanical analysis using the Flac-tp flow program in an attempt to distinguish the mechanisms active within the slope which were likely to produce the recorded pore water pressure.★medium to low compressibility★mid height★mine tailings dams e.g. This paper reviews these factors, covering the characteristics, types and magnitudes, environmental impacts, and remediation of mine tailings dam failures.★minimal e.g. The brown sand and gravel at depth were also omitted from the model as their effects on the surface failure were assumed to be minimal.★minimum e.g. This conceptual model allowed the deformation of elements within the slope to be kept to a minimum.★moisture content e.g. We use the Compound Topographic Index (CTI) to represent moisture content of the area.★model output★moment inertia★monitoring campaign★movement e.g. At this time the measured displacement showed a sharp up slope movement followed by a steady but increasing down slope movement; …when a sudden down slope movement was measured; the nature of the event was uncertain yet it could be seen that the increase in down slope movement occurred after the water level increase.★movement rates★null hypothesis e.g. We also use the p-values (defined as the probability of finding a test statistic value as great as the observed test statistic value, assuming that the null hypothesis is true) in order to assess the significance of each regression coefficient. In this case, the null hypothesis is that the regression coefficient is equal to zero. We reject the null hypothesis if the p-value is less than the significance value (α) we choose; here, we useα=0.001, corresponding to a 99% confidence level. Therefore if p<α, we reject the null hypothesis, and thereby assume that the regression coefficient is not equal to zero, and equals the computed value (Peng et al., 2002).★numerical studies e.g. Those numerical studies mentioned above successfully validated the usage of supplemental means for the full scale tests and also contributed to develop and optimize new type of rockfall barrier system effectively. However, very little research has been devoted to the more practical analysis of the optimal rockfall barrier system over the various unfavorable impact conditions which can usually happen in actual field conditions.★overlying★parametric study★peak ground acceleration e.g. Estimates of the peak ground acceleration (PGA) and peak ground velocity (PGV) for each event are adapted from the USGS Shakemap Atlas 2.0 (Garcia et al., 2012)★peak ground velocity★peak strengths★peak values of movement★periodic surface erosion★periodic walkover surveys★permeability★perspective e.g. Despite the shortcomings in site data from a modelers' perspective, the situation was typical of current instrumentation practice for a problem slope.★phreatic surface e.g. The slope, however, was observed to remain largely saturated for most of the year with a phreatic surface near or at the surface.★plasticity★plasticity index★pore pressure★pore pressure fluctuations★pore pressure transfer★pore pressure variations★pore water pressure★predictor variables e.g. We begin modeling by assessing qualitative relationships within the data, moving forward by using logistic regression as a statistical method for establishing a functional form between the predictor variables and the outcomes (Figure 3). We iterate over combinations of predictor variables and outcomes within the model, focusing first on one training event (Wenchuan, China), with the ultimate goal of expanding the analysis to global landslide datasets.★preferential drainage paths★previously e.g. As discussed previously,…★probability of landslide occurrence★profile★progressive failure 渐进破坏 e.g. (Abstract of a paper entitled “Progressive Failure of Lined Waste Impoundments”) “Progressive failure can occur along geosynthetic interfaces (土工合成材料界面) in lined waste landfills when peak strengths are greater than residual strengths. A displacement-softening formulation for geosynthetic interfaces was used in finite-elementanalyses of lined waste impoundments to evaluate the significance of progressive failure effects. First, the Kettleman Hills landfill was analyzed, and good agreement was found between the calculated and observed failure heights. Next, parametric analyses of municipal solid waste landfills were performed. Progressive failure was significant in all cases. Limit equilibrium analyses were also performed, and recommendations are provided for incorporating progressive failure effects in limit equilibrium analyses of municipal solid waste landfills”.★range★reference★reference grid point e.g. Due to the different grids of the Flac-tv flow model and the Shetran model there was no reference grid point, for which readings could be taken, at the exact same depth for both models. The closest similar reference points were at 1.91m depth for the Flac-tv flow model and 1.5 m depth for the Shetran model.★reliability e.g. Full scale rockfall tests to assess the reliability of the structure and also to investigate the interactions of the rockfall catchfence subjected to the impacts were carried out by Peila et al.★residual failure surface★residual friction angles★residual shear strength parameters★residual slope failure★residual strengths★restitution coefficient★rigid body mechaics★rock mass★rockfall barrier system e.g. Since the impact response of the rockfall catchfence has complicated phenomena caused by materials elastic and plastic behaviors of each member (i.e. steel post, nets and cables, etc.) and also influenced by various factors; such as impact angle, impact energy, dimension of block, strength of each member, mechanical stiffness of rockfall catchfence, etc., many researchers have devoted efforts to make a more comprehensive understanding of various facets of rockfall barrier system.★rockfall catchfences e.g. For the mitigation measure of rockfall hazards, rockfall catchfences are widely adapted in the potential hazard area to intercept and hold the falling materials.★rockfall hazards e.g. The road has been exposed to high potential rockfall hazards as a result of the fractured columnar natural slope condition with post tectonic joints.★rockfall protection kits★rockfall protection mesh★root cause★root cause of elevated pore pressure★rooting depth★rotational slope failure★saturated soils★seasonal pore pressure conditions★seasonal affects★seasonal fluctuations in embankment pore water pressures★section★shallow angle★shallow slips★shear strength★shear strength parameters e.g. In the second phase of the simulation, the shear strength parameters (c,f) were input into the model.★shortcomings e.g. Despite the shortcomings in site data from a modelers' perspective, the situation was typical of current instrumentation practice for a problem slope.★significantly e.g. These failures were sufficiently shallow that they did not significantly affect the overall stability of the slope.★simulate e.g. Furthermore, a parametric study was conducted on the permeability to get the best fit between recorded and simulated data.★site walkover survey★slightly e.g. There was a drop in water levels with the simulation but this occurred slightly before the recorded drop and the magnitude was approximately half of that recorded. The water levels within the simulation recovered at approximately the same time as the recorded water levels but the water levels peaked at just below the previous high at slightly under 6 m AOD; "This showed that for the latter half of the simulation there was no significant increase in rainfall; there was actually a slight decrease."★slip indicator readings★slip mass e.g. Assuming an average failure depth of 6 m, the total estimated volume of the slipped mass was in excess 18,900m3.★slip movement★slope★slope angle★slope crest★slope failure 边坡破坏★slope geometry★slope material properties e.g. The dynamic interaction between falling blocks and slope of the CRSP is calculated by empirically driven functions incorporating velocity, friction and slope material properties.★slope stability analysis★slope stability assessments e.g. The RS unit is suitable for testing both fully-softened shear strength and residual shear strength parameters that can be used for slope stability assessments of various scenarios.★slope-stability methods★slope toe★slope value e.g. Median, minimum, and maximum slope values calculated from Shuttle Radar Topography Mission (SRTM) elevation data by Verdian et al. (2007) are used in tests of the model.★soft clay★soil bearing capacity e.g. Analysis of slopes, embankments, and soil bearing capacity, on the other hand, requires good estimations of shear strength from peak to residual.★soil slope★soil stiffness e.g. Calculation of foundation settlement, for instance, requires a good estimation of soil stiffness at relatively small strains.★soil water characteristic curve e.g. There was limited information regarding the soil water characteristic curve of the materials.★soil wetness★stability★steep slope e.g. The same was true for the steep slope entering the river.★steep topographic slope e.g. Areas of steep topographic slope are often associated with active faulting and hence, likely areas of strong ground shaking.★stiffness★spatial distribution e.g. The spatial distribution of seismically induced landslides is dependent on certain physical characteristics of the area in which they occur.★study area e.g. The study area is located along route 5 in the boroughs of Fort Lee and Edgewater, Bergen County, NJ where high level of cliff, 10 to 27 m high, exists along the road as shown in Fig.1; The paper discusses a fundamental geology and geomechanics of the study area first and then statistical rockfall analysis using Colorado Rock Fall Simulation Program has been performed to estimate the critical impact condition and the capacity of rockfall barrier system required. Finally, a series of three dimensional dynamic finite element analyes is performed to provide additional verification of the design criterion made by CRSP analysis and to suggest the detailed design parameters to accommodate specific field conditions.★summarize e.g. The realistic and modeled root depth distributions are summarized in Fig.11 and vegetation properties are summarized in Table 3.★surface boundary condition★surface geology★surface irregularity★surface pore water pressure★surface roughness★swell-induced soil movements e.g. The developed correlations, along with the existing models, were then used to predict vertical soil swell movements of four case studies where swell-induced soil movements were monitored.★swell-induced volume changes★tailings e.g. Extraction of the targeted resource results in the concurrent production of a significant volume of waste material, including tailings, which are mixtures of crushed rock and processing fluids from mills, washeries or concentrators that remain after the extraction of economic metals, minerals, mineral fuels or coal; The volume of tailings is normally far in excess of the liberated resource, and the tailings often contain potentially hazardous contaminants; A priority for a reasonable and responsible mining organization must be to proactively isolate the tailings so as to forestall them from entering groundwaters, rivers, lakes and the wind.★tailings dams e.g. It is therefore accepted practice for tailings to be stored in isolated impoundments under water and behind dams.★tension crack of the slip★tension cracks★threshold e.g. For example, if we define 20% probability of a landslide to be the threshold, any probability equal to or greater than 20% will then be defined as a landslide prediction; By evaluating the percentage of true positives and true negatives from a model, we can decide upon the optimum-probability threshold for classification as a landslide prediction; this optimum value is in turn dependent upon the balance between high values of true positives and true negatives with low values of false positives and false negatives.★time interval★top boundary★top of the slope★topographic slope★topographical survey★unit weight data★unsaturated hydrological properties★unsaturated soils e.g. To date, however, there is very limited experimental evidence of unsaturated soil behavior under large deformations, and the corresponding residual shear strength properties, while the soil is being subjected to controlled-suction states.★upper slope★value e.g. Therefore low CTI values result from higher slope values and small drainage areas, whereas high CTI values result from lower slope values and larger drainage areas. Note that this value does not consider wetness contributed from the climate of an area, but is purely dependent on the topographic influence on wetness.★variation★volume change properties★water level e.g. The Shetran simulation showed that there was no reason for such a largewater level drop mid simulation and again no reason for a new higher water table during the latter half of the simulation; the low water levels occurred during the summer months, when evapotranspiration is highest; from the measured results it could be seen that an event took place which resulted in elevated water levels in the upper part of the lower slope; from Fig.16 it can be seen that the water levels below the upper slope increase by almost 4 m and the water levels at the BH105 location increase by just less than 1 m; such an increase corresponds to water levels in the latter period of monitoring.★water level variance★water regime e.g. From these preliminary analyses it could be seen that the water regime within the slope was governed by more than the surface processes investigated; therefore, a fully coupled hydromechanical model of the slope was run to see if any light could be shed on the pore water pressure regime.★water table e.g. The report stated that this water table rise occurred as a result of heavy rainfall.。

in the distance具体的中文解释in the distance的中文翻译英[in ðəˈdistəns] 美 [ɪn ði ˈdɪstəns]in the distance 基本解释在远处，在很远的那边in the distance的'单语例句1. The open air springs are surrounded by seasonal blooms of flowers and a view of green mountains looming in the distance.2. With fitness levels in the country declining officials are calling on more people to take part in long distance running events.3. In the distance stood glittering Canton Tower, completed just before the Asian Games and now the world's seventh tallest structure.4. I turn, and in the distance a small cavalcade of vans is slowly moving down the track.5. Costa Rican authorities have established a security perimeter around the entire prison in order to keep curious bystanders on a safe distance from the center.6. Tseng said the goal of the swing change was to maintain her distance but cut down on the effort needed in each swing.7. The zoo added customized steel mesh over the bars, built in a feeding chute and increased the distance between the public and the cats.8. The parks will come in different sizes and formats and might become the neighborhood park within people's walking distance.in the distance的双语例句1. In this research at first the six factors affecting rainfall were chosen, as the input variables. They are the minimum atomosphericpressure, maximum wind velocity near typhoon center, move speed of typhoon center, the radius of typhoon, the shortest distance between typhoon center and Taipei monitoring station, station humidity.本研究先选取影响台风雨之因子，选用钟型函将中心最低气压、近中心最大风速、移动速度、暴风半径、台风中心距测站最短距离、测站湿度做为六个输入变，建模糊属函。

英语统计图作文语句Title: Analyzing the Trends: A Statistical Exploration.In the realm of data analysis, statistical graphs serve as powerful tools to visualize and interpret patterns, trends, and relationships within a dataset. They enable us to gain insights into complex data, often revealing hidden patterns and trends that might otherwise remain unnoticed. In this article, we delve into the intricacies ofstatistical graphs, discussing their types, applications, and the insights they offer.Types of StatisticalGraphs.Statistical graphs are diverse and each type offers a unique perspective on the data. The most common types include line graphs, bar graphs, pie charts, scatter plots, and histograms.Line graphs are effective in depicting changes overtime, showing the trend of a variable over a period. They are particularly useful in identifying patterns such as seasonal variations or long-term trends.Bar graphs, on the other hand, are excellent for comparing values across different categories. They allow us to visualize the relative sizes of different groups or categories, making it easier to identify outliers or outliers.Pie charts are useful for representing the proportionate distribution of data. They divide a circle into sectors, each representing a proportion of the whole, enabling quick visualization of the relative sizes of different components.Scatter plots are valuable tools for understanding the relationship between two variables. By plotting the values of two variables against each other, patterns and correlations can be easily identified.Histograms provide a frequency distribution ofnumerical data. They group data into intervals and display the number of observations falling into each interval, revealing the shape, distribution, and spread of the data.Applications of StatisticalGraphs.Statistical graphs find applications across various fields, including business, science, medicine, and social sciences. In business, line graphs and bar graphs are often used to track sales performance, analyze market trends, or compare product sales across different regions. In science, scatter plots and histograms are essential forunderstanding the relationship between variables and identifying patterns in experimental data. In medicine, statistical graphs are used to monitor patient outcomes, analyze epidemiological data, and assess the effectivenessof treatments. In social sciences, they are employed to understand population distributions, identify social trends, and evaluate policies and programs.Insights Offered by StatisticalGraphs.Statistical graphs offer a visual representation of data, making it easier to identify patterns, trends, and relationships. They enable us to quickly compare values across different categories, understand the distribution of data, and assess the strength of relationships between variables. Furthermore, they can help us identify outliers or unexpected values that might indicate errors or unusual occurrences. By providing a visual representation of the data, statistical graphs can also enhance understanding and communication among stakeholders, making complex data more accessible and comprehensible.In conclusion, statistical graphs are indispensable tools for analyzing and understanding data. By utilizing different types of graphs, we can gain valuable insights into patterns, trends, and relationships within a dataset. These insights can inform decision-making, lead to better understanding, and foster collaboration among stakeholders. As the world becomes increasingly data-driven, the importance of statistical graphs in extracting meaningful information from data cannot be overstated.。

修正的移动平均法计算公式例题English Answer:Definition: Seasonal variations are recurring patterns in time series data that occur on a regular basis within a year. This seasonality can be daily, weekly, monthly, or quarterly.Example: A clothing store may see a spike in sales during the holiday season each year. This is an example of a seasonal variation that occurs annually.Challenges of Seasonality:Seasonality can make it difficult to forecast future values of time series data.It can also lead to inaccurate conclusions about the underlying trend of the data.Decomposition of Time Series:To account for seasonality, time series data can be decomposed into three components:Trend: The long-term, underlying pattern of the data.Seasonality: The recurring pattern within a year.Irregularity: Random fluctuations not explained by the trend or seasonality.Statistical Methods for Detecting Seasonality:Several statistical methods can be used to detect seasonality in time series data:Autocorrelation: This measure determines the correlation between a time series and its lagged values. Seasonality is often indicated by high autocorrelation at specific lags corresponding to the seasonal period.Periodogram: This analysis method identifies the frequencies at which the data varies. Seasonality is evident in the presence of strong peaks at frequencies corresponding to the seasonal period.Correction for Seasonality:Once seasonality is detected, it can be corrected using various methods:Seasonal Decomposition: The time series is decomposed into its trend, seasonal, and irregular components. The seasonal component can then be removed or adjusted to stabilize the data.Differencing: This method involves subtracting a previous value of the time series from the current value. Seasonality is often captured in the differenced series, making it easier to forecast.Smoothing: Techniques such as moving averages or exponential smoothing can be applied to smooth out theseasonal variations and reveal the underlying trend.Example of Seasonal Correction:Consider a dataset representing monthly sales of a product. The following steps illustrate how seasonality can be corrected:1. Detect Seasonality: Calculate the autocorrelation and periodogram to confirm the presence of seasonality.2. Decompose the Data: Use seasonal decomposition to separate the data into trend, seasonal, and irregular components.3. Remove Seasonality: Subtract the seasonal component from the original data.4. Forecast: Use the deseasonalized data to forecast future sales, excluding seasonal variations.Conclusion:Accounting for seasonality in time series analysis is crucial for accurate forecasting and data interpretation. By detecting and correcting seasonality, analysts can gain a clearer understanding of the underlying trends and patterns in the data, leading to improved decision-making.Chinese Answer:季节性是时间序列数据中周期性的重复模式，它在一年内会定期发生。

2024年高三英语统计学分析单选题30题1.The average height of a group of people is calculated by adding up all the heights and then dividing by the _____.A.number of peopleB.sum of heightsC.difference in heightsD.product of heights答案：A。

本题考查平均数的计算方法。

平均数是所有数据之和除以数据的个数，这里就是把所有人的身高加起来然后除以人数。

选项B“sum of heights”是身高总和，不是计算平均数的除数。

选项C“difference in heights”是身高差，与平均数计算无关。

选项D“product of heights”是身高乘积，也与平均数计算无关。

2.In a statistical survey, the mode is the value that _____.A.appears most frequentlyB.has the highest sumC.is the averageD.is the middle value答案：A。

本题考查众数的概念。

众数是一组数据中出现次数最多的数值。

选项B“has the highest sum”是和最大，与众数无关。

选项C“is the average”是平均数，与众数不同。

选项D“is the middle value”是中位数，不是众数。

3.The median of a set of data is found by arranging the data in orderand then finding the _____.rgest valueB.smallest valueC.middle valueD.average value答案：C。

全景版：环境监测布局英文版Title: Comprehensive Version: Environmental Monitoring LayoutIntroduction:In this document, we will discuss the layout of environmental monitoring in a comprehensive manner. Environmental monitoring plays a crucial role in ensuring the protection and preservation of our natural surroundings. By strategically placing monitoring stations, we can effectively gather data on various environmental parameters and take necessary actions to mitigate any negative impacts on the environment.Importance of Environmental Monitoring:Environmental monitoring is essential for assessing the health of ecosystems, tracking changes over time, and identifying potential risks to human health and the environment. It allows us to monitor air quality, water quality, soil contamination, and biodiversity, among other factors. By analyzing the data collected through monitoring, we can makeinformed decisions to protect and conserve our environment for future generations.Key Components of Environmental Monitoring Layout:1. Selection of Monitoring Parameters:- Determine the specific environmental parameters to be monitored, such as air pollutants, water quality indicators, noise levels, and habitat conditions.- Consider the regulatory requirements and scientific significance of each parameter to prioritize monitoring efforts.2. Location of Monitoring Stations:- Identify suitable locations for monitoring stations based on the distribution of potential environmental hazards and the accessibility of monitoring sites.- Ensure that monitoring stations are strategically placed to capture representative data for the target environmental parameters.3. Frequency of Monitoring:- Establish a monitoring schedule that balances the need for frequent data collection with resource constraints.- Consider seasonal variations and long-term trends when determining the frequency of monitoring activities.4. Data Collection and Analysis:- Implement standardized protocols for data collection to ensure consistency and reliability of monitoring results.- Use advanced analytical tools to process and interpret monitoring data, such as GIS mapping and statistical modeling.5. Communication and Reporting:- Share monitoring results with stakeholders, including regulatory agencies, local communities, and environmental organizations.- Present monitoring data in a clear and accessible format to facilitate understanding and decision-making.Conclusion:A well-designed environmental monitoring layout is essential for effectively assessing and managing environmental risks. By following a comprehensive approach to environmental monitoring, we can enhance our understanding of environmental processes, safeguard natural resources, and promote sustainable development. Let's continue to prioritize environmental monitoring efforts to protect our planet for future generations.。

高三英语统计学分析单选题30题1.The purpose of statistics is to collect, analyze and present ___.A.datarmationC.numbersD.results答案：A。

本题主要考查统计学中“统计的目的是收集、分析和呈现什么”。

选项A“data”（ 数据）符合统计学的定义，统计就是对数据进行处理。

选项B“information”（信息）比较宽泛，统计学主要针对具体的数据。

选项C“numbers”（ 数字）只是数据的一种表现形式，不全面。

选项D“results”（结果）不准确，统计的目的不是单纯呈现结果，而是通过数据来呈现。

2.In statistics, a sample is a subset of ___.A.the populationB.a groupC.peopleD.items答案：A。

在统计学中，样本是总体的一部分。

选项A“the population” 总体）正确。

选项B“a group” 一组）不确切。

选项C“people” 人）太局限。

选项D“items” 物品）也不准确。

3.Statistics helps us make inferences about a population based on ___.A.assumptionsB.samplesC.guessesD.estimates答案：B。

统计学帮助我们基于样本对总体进行推断。

选项B“samples”（样本）正确。

选项A“assumptions”（假设）不准确。

选项C“guesses”（猜测）不科学。

选项D“estimates”（估计）只是其中一方面，不全面。

4.The mean is a measure of ___.A.central tendencyB.variabilityC.distributionD.skewness答案：A。

均值是集中趋势的一种度量。