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HW2 sol - 2.5(a The five-number summary is Min = 23,040...

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2.5 (a) The five-number summary is Min = 23,040, Q1=30,315, M=31,975, Q3=32,710, Max=33,650. (b) Note the distances between the numbers in the five-number summary: In order, the gaps are 7275, 1660, 735, and 940 pounds. That the first two gaps are larger gives some indication of the left skew. 2.9 (a) x_mean=32.4/6=5.4mg of phosphate per deciliter of blood. (b) The standard deviation is s=sqrt(2.06/5)=0.6419mg/dl. 2.11 (a) Not appropriate : the distribution of percents of college graduates has a hight outlier. (b) x_mean and s are fine: The Iowa Test score distribution is quite symmetric and has no outliers. (b) Not appropriate : The wood breaking-strength distribution is strongly skewed. 2.25 (a) The mean will be greater than the median because of the right skew. We find that x_mean=251.9 and M=236 doctors per 100,000 people. (b) Outliers have a greater effect on the mean, so removing D.C. should change x_mean more than M. Indeed, we find that x_mean^* (^* means a superscript)=243.26 and M^*=234.5 doctors per 100,000 people – x_mean decreased by about 8.6 while the median changed by 1.5.

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