Question

1. during the last 15 years of his baseball career, andrew hit the following number of home runs each season. 35, 24, 32, 36, 40, 32, 40, 38, 36, 33, 11, 20, 19, 22, 8

a. state and label the values of the minimum, 1st quartile, median, 3rd quartile, and maximum.

Explanation:

Step1: Arrange data in ascending order

8, 11, 19, 20, 22, 24, 32, 32, 33, 35, 36, 36, 38, 40, 40

Step2: Find the minimum

The minimum is the smallest value. Minimum = 8

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

There are $n = 15$ data points. The position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{15+1}{4}=4$. So $Q_1$ is the 4th value in the ordered list. $Q_1 = 20$

Step4: Find the median

The position of the median for $n = 15$ (odd number of data points) is $i=\frac{n + 1}{2}=\frac{15+1}{2}=8$. So the median is the 8th value in the ordered list. Median = 32

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

The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So $Q_3$ is the 12th value in the ordered list. $Q_3 = 36$

Step6: Find the maximum

The maximum is the largest value. Maximum = 40

Answer:

Minimum: 8, 1st quartile: 20, Median: 32, 3rd quartile: 36, Maximum: 40