Question

mickey mantle played for the new york yankees for 18 years. here is the number of home runs by mantle per year: 13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18 compute the five - number summary of the data and determine which boxplot would best represent the data. a. b. c. d.

Explanation:

Step1: Sort the data

First, sort the data set \(13,23,21,27,37,52,34,42,31,40,54,30,15,35,19,23,22,18\) in ascending order: \(13,15,18,19,21,22,23,23,27,30,31,34,35,37,40,42,52,54\)

Step2: Find the minimum value

The minimum value (\(Min\)) of the sorted data set is \(13\)

Step3: Find the first - quartile (\(Q_1\))

Since \(n = 18\) (the number of data points), \(n/4=4.5\). The first - quartile \(Q_1\) is the average of the \(4^{th}\) and \(5^{th}\) values. The \(4^{th}\) value is \(19\) and the \(5^{th}\) value is \(21\). So \(Q_1=\frac{19 + 21}{2}=20\)

Step4: Find the median (\(Q_2\))

Since \(n = 18\), \(n/2 = 9\). The median \(Q_2\) is the average of the \(9^{th}\) and \(10^{th}\) values. The \(9^{th}\) value is \(27\) and the \(10^{th}\) value is \(30\). So \(Q_2=\frac{27+30}{2}=28.5\)

Step5: Find the third - quartile (\(Q_3\))

Since \(3n/4 = 13.5\). The third - quartile \(Q_3\) is the average of the \(13^{th}\) and \(14^{th}\) values. The \(13^{th}\) value is \(35\) and the \(14^{th}\) value is \(37\). So \(Q_3=\frac{35 + 37}{2}=36\)

Step6: Find the maximum value

The maximum value (\(Max\)) of the sorted data set is \(54\)

Now, check the box - plots:

• The minimum value is \(13\), the first - quartile \(Q_1 = 20\), the median \(Q_2=28.5\), the third - quartile \(Q_3 = 36\), and the maximum value is \(54\)

Answer:

a.