# Chap03 - Solutions to End-of-Section and Chapter Review...

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Solutions to End-of-Section and Chapter Review Problems 213 CHAPTER 3 3.1 (a) Mean = 6 Median = 7 There is no mode. (b) Range = 7 Variance = 8.5 Interquartile range = 5.5 Standard deviation = 2.915 Coefficient of variation = (2.915/6)•100% = 48.6% (c) Since the mean is less than the median, the distribution is left-skewed. 3.2 (a) Mean = 7 Median = 7 Mode = 7 (b) Range = 9 Variance = 10.8 Interquartile range = 5 Standard deviation = 3.286 Coefficient of variation = (3.286/7)•100% = 46.94% (c) Since the mean equals the median, the distribution is symmetrical. 3.3 (a) Mean = 6 Median = 7 Mode = 7 (b) Range = 12 Variance = 16 Interquartile range = 6 Standard deviation = 4 Coefficient 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 = 2 Median = 7 Mode = 7 (b) Range = 17 Variance = 62 Interquartile range = 14.5 Standard deviation = 7.874 Coefficient 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 1 Set 2 Mean 4 14 Median 3 13 Mode 2 12 (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 1 Set 2 Range 8 8 Interquartile range 3 3 Variance 8.33* 8.33* Standard deviation 2.89* 2.89* Coefficient of variation 72.25% 20.64% *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 the exception 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 is 10 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.

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214 Chapter 3: Numerical Descriptive Measures 3.5 (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 ( 29 ( 29 1/ 2 1 0.1 1 0.3 1 19.58% G R = + + - = 3.7 (a) Grade X Grade Y Mean 575 575.4 Median 575 575 Standard deviation 6.40 2.07 (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 much smaller. The range in values for Grade Y is 5 mm compared to the range in values for Grade X which is 16 mm.
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## This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue.

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Chap03 - Solutions to End-of-Section and Chapter Review...

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