Chapter 1.3, Problem 110E

(a)

To determine

To explain the out of the male and female doctors which have more symmetrical shape.

Answer to Problem 110E

Right skewed

Explanation of Solution

Given:

The output:

  

The difference between the first quartile and median and between the median and third quartile is approximately same for Female doctors and in case of Male doctors the difference between the median and third quartile is more than the difference between the first quartile and median. That indicates that the distribution of male doctors is Right or positively skewed.

(b)

To determine

To compare the interquartile range of both datasets.

Explanation of Solution

Formula used:

  ${\text{Interquartile Range = Q}}_3-{\text{Q}}_1$

Calculation:

  $\begin{array}{c}{\text{For Male(IQR) = Q}}_3-{\text{Q}}_1\\ =50-27\\ =23\end{array}$

  $\begin{array}{c}{\text{For Female(IQR) = Q}}_3-{\text{Q}}_1\\ =29-10\\ =19\end{array}$

The interquartile range for the Male and female is not so different but the standard deviation for Males is too large as compared to the Females that are because the Males data contains the outliers while female dataset does not.

(c)

To determine

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

Answer to Problem 110E

Male’s data contains the outliers

Female’s data not contains the outliers

Explanation of Solution

Calculation:

  $\begin{array}{l}\text{Males:}\\ {\text{Outliers > Q}}_{\text{3}}+1.5\text{IQR}\\ \text{Outliers > 50 + 1}\text{.5 }\times (23)\\ \text{Outliers > 84}\text{.5}\\ \\ {\text{Outliers < Q}}_1-1.5\text{IQR}\\ \text{Outliers <27 - 1}\text{.5 }\times (23)\\ \text{Outliers < }-7.5\end{array}$

  $\begin{array}{l}\text{Females:}\\ {\text{Outliers > Q}}_{\text{3}}+1.5\text{IQR}\\ \text{Outliers > 29 + 1}\text{.5 }\times (19)\\ \text{Outliers > 57}\text{.5}\\ \\ {\text{Outliers < Q}}_1-1.5\text{IQR}\\ \text{Outliers <10 - 1}\text{.5 }\times (19)\\ \text{Outliers < -18}\text{.5}\end{array}$

The maximum value of the Male data falls beyond the range [-19.925, 84.595]. That indicates that the Male data contains the outliers. While the female data does not contains any outlier.