Explanation Given: The following are the numbers of home runs hit by the home run champions in the National League for the years 1975 to 1989 and for 2001 to 2015. a) 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 b) 2001–2015: 73, 49, 47, 48, 51, 58, 50, 48, 47, 42, 39, 41, 36, 37, 42 Graph: i) Consider the given frequency distribution table, 1975–1989: 38, 38, 52, 40, 48, 48, 31, 37, 40, 36, 37, 37, 49, 39, 47 The minimum value in the data set is 31 and maximum value is 52. For finding the median first arrange the data set in increasing order, 31 , 36 , 37 , 37 , 37 , 38 , 38 , 39 , 40 , 40 , 47 , 48 , 48 , 49 , 52 The median is the middle value. The data set has 15 values. So, the middle value is 15 + 1 2 = 16 2 = 8 t h value. 31 , 36 , 37 , 37 , 37 , 38 , 38 _ Lower half , 39 _ m e d i a n , 40 , 40 , 47 , 48 , 48 , 49 , 52 _ Upper half The median is 39. First quartile is the median of lower half values. Lower half has 7 values. Therefore, first quartile is given by 4 th value in the lower half which is seen in the above step. So, first quartile is 37. Third quartile is the median of upper half values. Upper half has 7 values. Therefore, third quartile is given by 4 th value in the upper half which is seen in the above step. So, third quartile is 48. Five number summary is, Minimum 31 First quartile 37 Median 39 Third quartile 48 Maximum 52 Steps for construction of Box-whiskers plot 1. Determine the values for the five-number summary. 2. Draw a horizontal axis from the minimum value to the maximum value. 3. Draw a rectangular box over the axis from Q 1 to Q 3 . The height of the box is not important. 4. Draw a vertical line in the box where the median is located (note that it might not be in the middle of the box). 5. Draw horizontal lines extending from the edges of the boxes (the quartiles) to the minimum and maximum values. These are the whiskers. Five number summary is 31, 37, 39, 48, 52

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ISBN: 9780134506470

Author: Pirnot

Publisher: PEARSON

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Chapter 14.2, Problem 39E

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The box-and-whisker plots for the distributions of the number of home runs hit for the two given time periods in Example 6 in Section 14.1.

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Chapter 14.2, Problem 38E

Chapter 14.2, Problem 40E

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To graph: The box-and-whisker plots for the distributions of the number of home runs hit for the two given time periods in Example 6 in Section 14.1.

Solution Summary: The author illustrates the box-and-whisker plots for the distributions of the number of home runs hit by the home run champions in the National League for 1975 to 1989 and 2001 to 2015.

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To graph: The box-and-whisker plots for the distributions of the number of home runs hit for the two given time periods in Example 6 in Section 14.1.

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Chapter 14 Solutions

To graph:

The box-and-whisker plots for the distributions of the number of home runs hit for the two given time periods in Example 6 in Section 14.1.