chap03.doc - Solutions to End-of-Section and Chapter Review...

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Solutions to End-of-Section and Chapter Review Problems 75CHAPTER 33.1(a)Mean = 6Median = 7There is no mode.(b)Range = 7Variance = 8.5Interquartile range = 5.5Standard deviation = 2.915Coefficient of variation = (2.915/6)•100% = 48.59%(c)Since the mean is less than the median, the distribution is left-skewed.3.2(a)Mean = 7Median = 7Mode = 7(b)Range = 9Variance = 10.8Interquartile range = 5Standard deviation = 3.286Coefficient of variation = (3.286/7)•100% = 46.94%(c)Since the mean equals the median, the distribution is symmetrical.3.3(a)Mean = 6Median = 7Mode = 7(b)Range = 12Variance = 16Interquartile range = 6Standard deviation = 4Coefficient of variation = (4/6)•100% = 66.67%(c)Since the mean is less than the median, the distribution is left-skewed.3.4(a)Mean = 2Median = 7Mode = 7(b)Range = 17Variance = 62Interquartile range = 14.5Standard deviation = 7.874Coefficient of variation = (7.874/2)•100% = 393.7%(c)Since the mean is less than the median, the distribution is left-skewed.3.5(a)Set 1Set 2Mean414Median313Mode212(b)-(c)The data values in Set 2 are each 10 more than the corresponding values in Set 1.The measures of central tendency for Set 2 are all 10 more than the comparable statistics for Set 1.(d) Set 1Set 2Range88Interquartile range33Variance8.33*8.33*Standard deviation2.89*2.89*Coefficient of variation72.17%20.62%*Note:Slight differences are due to rounding.(e) Since the mean is greater than the median for each data set, the distributions are both right-skewed.(f) Because the data values in Set 2 are each 10 more than the corresponding values in Set 1, the measures of spread among the data values remain the same across the two sets, with theexception of the coefficient of variation. The coefficients of variation are different because the sample standard deviation is divided by the set’s mean; in the case of Set 2, the mean is10 more than the mean for Set 1, resulting in a larger denominator and a smaller coefficient. Set 2 is a reflection of Set 1 simply shifted up the scale 10 units, so the distributions are also reflections of each other.
76 Chapter 3: Numerical Descriptive Measures3.5(g) Generally stated, when a second data set is an additive shift from an original set, the cont.measures of central tendency for the second set are equal to the comparable measures for the original set plus the value, or distance, of the shift; the measures of spread for the second set are equal to the corresponding measures for the original set, with the exception of the coefficient of variation; the shape of the second distribution will be a reflection of the shape of the original distribution.3.6 1/ 210.110.3119.58%GR3.7(a)Grade X Grade YMean575575.4Median575575Standard deviation6.402.07(b) If quality is measured by the average inner diameter, Grade X tires provide slightly better quality because X’s mean and median are both equal to the expected value, 575 mm. If, however, quality is measured by consistency, Grade Y provides better quality because, even though Y’s mean is only slightly larger than the mean for Grade X, Y’s standard deviation is

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