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WCU ECO 251 - ECO 251 Study Notes

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251dscr_D 9/25/02 (Open this document in 'Outline' view!)Appendix D: Review5. Reviewa. Grouped Data.Solution:b. Ungrouped Data.Solution:251dscr_D 9/25/02 (Open this document in 'Outline' view!)Appendix D: Review 5. Reviewa. Grouped Data. Consider the following sample: Class f 0.5 - 1.5 1 1.5 - 2.5 0 2.5 - 3.5 1 3.5 - 4.5 2 a. Calculate the meanb. Calculate the variance and standard deviationc. Calculate and interpret the skewness and relative skewnessd. Calculate and interpret Pearson's measure of skewnesse. Calculate the medianf. Calculate the interquartile rangeSolution:You need the following: Class x(midpoint) f F fx 2fx 3fx 0.5 - 1.5 1 1 1 1 1 1 1.5 - 2.5 2 0 1 0 0 0 2.5 - 3.5 3 1 2 3 9 27 3.5 - 4.5 4 2 4 8 32 128 4 12 42 156Note:  ,4nf12fx, ,422fx1563fx.a. Calculate the mean 3412nfxxb. Calculate the variance and standard deviation  2363344212222nxnfxs414.12variance s 471.032xsCc. Calculate and interpret* the skewness and relative skewness  323323)2)(1(xnfxxfxnnnk       33424233156)2)(3(4 6324 . 414.1243331skgd. Calculate and interpret* Pearson's measure of skewness The mode is 4, since that occurs most.   121.22433.3deviationstdmodemeanSK2e. Calculate the median First use  1 npposition , then usewfFpNLxppp1 to find the value. Here 5.p. So    5.255.1 np. This location is above 2 and below 4, so use the class 3.5 to 4.5. Then  5.312245.5.35.x.f. Calculate the interquartile range For the first quartile    25.1525.1  npposition. This location is above 1 and below2 , so use the class 2.5 to 3.5. Then, using the second formula, we find 5.2111425.5.2175.Qx For the third quartile    75.3575.1 np. This location is above 2 and below 4, so use the class 3.5 to 4.5. Then, we find  0.4122475.5.3325.Qx. 5.15.20.413  QQIQRb. Ungrouped Data. Consider the following sample: 1, 3, 4, 4 -which can also be written as x 1x 1 2x 3 3x 4 4x 4 a. Calculate the meanb. Calculate the variance, standard deviation and coefficient of variation.c. Calculate and interpret the skewness and relative skewnessd. Calculate and interpret Pearson's measure of skewnesse. Calculate the medianf. Calculate the interquartile rangeSolution:You need the following: x 2x 3x 1x 1 1 1 2x 3 9 27 3x 4 16 64 4x 4 16 64 12 42 156Note: ,4n12x, ,422x1563x.a. Calculate the mean 3412nxx3b. Calculate the variance and standard deviation  2363344212222nxnxs414.12variance s 471.032xsCc. Calculate and interpret* the skewness and relative skewness  323323)2)(1(xnxxxnnnk       33424233156)2)(3(4 6324 . 414.1243331skgd. Calculate and interpret* Pearson's measure of skewness The mode is 4, since that occurs most.   121.22433.3deviationstdmodemeanSKe. Calculate the median First use  banpposition .1  , then use aaapxxbxx  11. to find the value. Here5.p. So    5.255.1 np. Thus 2a and 5.0. b. So, using the second formula,     .5.3345.035.05.023221225.xxxxxxxf. Calculate the interquartile range For the first quartile    25.1525.1  npposition. Thus 1a and 25.0. b. So     .5.11325.0125.025.01121111175.xxxxxxQx For the third quartile    75.3575.1 np. Thus 3a and 75.0. b. So     .44475.0475.075.03343313325.xxxxxxQx 5.25.10.413  QQIQR* These negative numbers all indicate skewness to the


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