Chapter 1.3, Problem 109E

(a)

To determine

To explain the shape of the data based on the given output.

Answer to Problem 109E

Right skewed

Explanation of Solution

Given:

The output:

  

Based on the given output, it is clearly known that Mean is more than the median, and in case of Right skewed dataset the mean is more than the median. Therefore, the shape of the given data is Right skewed.

(b)

To determine

To explain the standard deviation of the given data.

Explanation of Solution

The standard deviation of the given data is equal to 21.70, the standard deviation shows the average distance between the each point from the mean of the given data set. The standard deviation is the measure of spread which defines the how the data is scattered from the mean.

(c)

To determine

To explain whether the given data includes the outliers or not.

Answer to Problem 109E

Dataset contains the outliers

Explanation of Solution

Calculation:

  $\begin{array}{l}{\text{Outliers > Q}}_{\text{3}}+1.5\text{IQR}\\ \text{Outliers > 45}\text{.40 + 1}\text{.5 }\times (45.40-19.27)\\ \text{Outliers > 84}\text{.595}\\ \\ {\text{Outliers < Q}}_1-1.5\text{IQR}\\ \text{Outliers <19}\text{.27 - 1}\text{.5 }\times (45.40-19.27)\\ \text{Outliers < -19}\text{.925}\end{array}$

The maximum value of the given data falls beyond the range [-19.925, 84.595]. That indicates that the given data contains the outliers.