Question

use the accompanying data set to complete the following actions.
a. find the quartiles.
b. find the interquartile range.
c. identify any outliers.
40 50 36 44 42 36 39 48 44 39 36 55 43 36 15 50 37 50 30 29
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: Sort the data set

First, sort the data set in ascending order: 15, 29, 30, 36, 36, 36, 36, 36, 37, 39, 39, 40, 42, 43, 44, 44, 48, 50, 50, 50, 55.

Step2: Calculate the position of Q2 (median)

There are $n = 21$ data - points. The position of the median $Q_2$ is $\frac{n + 1}{2}=\frac{21+1}{2}=11$. So, $Q_2$ is the 11th value in the sorted data set, and $Q_2 = 39$.

Step3: Calculate the position of Q1

The lower - half of the data set consists of the first 10 values. The position of $Q_1$ is $\frac{10 + 1}{2}=5.5$. So, $Q_1=\frac{36+36}{2}=36$.

Step4: Calculate the position of Q3

The upper - half of the data set consists of the last 10 values. The position of $Q_3$ is $\frac{10 + 1}{2}=5.5$. So, $Q_3=\frac{44+44}{2}=44$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=44 - 36 = 8$.

Step6: Identify outliers

The lower fence for outliers is $Q_1-1.5\times IQR=36-1.5\times8=36 - 12 = 24$. The upper fence for outliers is $Q_3 + 1.5\times IQR=44+1.5\times8=44 + 12 = 56$. The value 15 is less than 24, so 15 is an outlier.

Answer:

a. The first quartile, $Q_1$, is 36
The second quartile, $Q_2$, is 39
The third quartile, $Q_3$, is 44
b. The inter - quartile range is 8
c. The outlier is 15