Question

Weights aren’t Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged $20$ to $29$ have mean $141.7$ pounds and median $133.2$ pounds. The first and third quartiles are $118.3$ pounds and $157.3$ pounds. What can you say about the shape of the weight distribution? Why?

Short answer

The distribution is right-skewed.

Step-by-step solution

Given Information

The weights of women aged$=20to29$

Mean$=141.7pounds$

Median$=133.2pounds$

The first and third quartiles$=118.3pounds$

The third quartiles$=157.3pounds$

Explanation

Here are the steps to find the distribution of weights:

• Due to the unequal mean and median, the shape of the weight distribution is skewed.
• A right-skewed distribution is also evident since the mean is greater than the median and large values influence the mean.

In other words, the distribution of income is right-skewed.