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. boxplot a description b. boxplot b description c. boxplot c description d. boxplot d description please select the best answer from the choices provided

Explanation:

Step1: Sort the data

$13,15,18,19,21,22,23,23,27,30,31,34,35,37,40,42,52,54$

Step2: Find the minimum

The minimum value is $13$.

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

There are $n = 18$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{18+1}{4}=4.75$. So, $Q_1=19+(21 - 19)\times0.75 = 20.5$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{18 + 1}{2}=9.5$. So, $Q_2=\frac{27+30}{2}=28.5$.

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

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(18+1)}{4}=14.25$. So, $Q_3=35+(37 - 35)\times0.25=35.5$.

Step6: Find the maximum

The maximum value is $54$.

Step7: Analyze box - plots

The box - plot should have the minimum at $13$, $Q_1$ at $20.5$, median at $28.5$, $Q_3$ at $35.5$ and maximum at $54$.

Answer:

a.