Question

use the accompanying data set to complete the following actions.
a. find the quartiles.
b. find the interquartile range.
c. identify any outliers.

83 81 88 93 87 65 90 86 87 80 80 83 80 84 80 88

a. find the quartiles.
the first quartile, q1, is
the second quartile, q2, is
the third quartile, q3, is
(type integers or decimals.)

Explanation:

Step1: Arrange data in ascending order

00, 00, 00, 00, 00, 00, 01, 03, 03, 03, 04, 05, 05, 07, 07, 08

Step2: Find the median (Q2)

There are 16 data - points. The median is the average of the 8th and 9th ordered values. So, $Q_2=\frac{03 + 03}{2}=03$.

Step3: Find the lower half for Q1

The lower half of the data is 00, 00, 00, 00, 00, 00, 01, 03. The median of this lower - half (Q1) is the average of the 4th and 5th ordered values. So, $Q_1=\frac{00+00}{2}=00$.

Step4: Find the upper half for Q3

The upper half of the data is 03, 04, 05, 05, 07, 07, 08. The median of this upper - half (Q3) is the average of the 4th and 5th ordered values. So, $Q_3=\frac{05 + 05}{2}=05$.

Answer:

The first quartile, $Q_1$ is 00
The second quartile, $Q_2$ is 03
The third quartile, $Q_3$ is 05