Chapter 2.2, Problem 68E

To determine

To explain:about the shape of the weight distribution

Answer to Problem 68E

Women's weights are skewed to the right:

Explanation of Solution

Given:

Mean 141.7 pounds and median 133.2 pounds (age: 20 to 29)

The first and third quartiles are 118.3 pounds and 157.3 pounds.

Calculation:

The weights of women have the following summary statistics:

  $\begin{array}{l}M=133.2\\ Q_1=118.3\\ Q_3=157.3\end{array}$

Women's weights are skewed to the right: This makes the mean higher than the median, and it is also revealed in the differences:

  $\begin{array}{l}M-Q_1=133.2-118.3\\ =14.9\text{pounds}\end{array}$

And

  $\begin{array}{l}{Q}_3-M=157.3-133.2\\ =24.1\text{pounds}\end{array}$

Conclusion:

Therefore, women's weights are skewed to the right: