Chapter 1.3, Problem 108E

To determine

To identify the outliers if any.

Answer to Problem 108E

No outlier found in the given data.

Explanation of Solution

Given:

Mean = 3.2

Standard deviation = 1.9

  

Formula used:

  $\begin{array}{l}{\text{Outliers > Q}}_{\text{3}}+1.5\text{IQR}\\ {\text{Outliers < Q}}_1-1.5\text{IQR}\end{array}$

Calculation:

From the question 102:

First quartile = 16

Third quartile = 28

Interquartile Range: 12

Now,

  $\begin{array}{l}{\text{Outliers > Q}}_{\text{3}}+1.5\text{IQR}\\ \text{Outliers > 28 + 1}\text{.5 }\times 12\\ \text{Outliers > 46}\\ \\ {\text{Outliers < Q}}_1-1.5\text{IQR}\\ \text{Outliers <16 - 1}\text{.5}\times 12\\ \text{Outliers < -2}\end{array}$

It shows that any value that away from the range of -2 to 46, will be considered as the outlier and based on the given dot plot, it can easily observed that no value falls beyond this range.