Question

box-and-whisker plot which of the following statements are true? check all of the boxes that apply. the female dog graph is skewed. the range for female dogs is much larger than the range for male dogs. the female dog data is best represented by the median. the female dog data is less skewed than the male dog data. image of box-and-whisker plot with male (orange) and female (blue) dogs, x - axis: weight (lb) from 40 to 100 done

Explanation:

To solve this, we analyze each statement using box - and - whisker plot concepts:

Step 1: Analyze "The female dog graph is skewed."

In a box - and - whisker plot, if the median is not in the center of the box or the whiskers are of different lengths, the data is skewed. Looking at the female dog's box - and - whisker plot, the median (the line inside the box) is not in the middle of the box, and the whiskers have different lengths. So, the female dog's data is skewed. This statement is true.

Step 2: Analyze "The range for female dogs is much larger than the range for male dogs."

The range of a data set in a box - and - whisker plot is calculated as the maximum value minus the minimum value. For male dogs, let's assume the minimum is around 40 and the maximum is around 100 (from the plot). For female dogs, the minimum is around 40 and the maximum is around 100 as well (visually). So, the ranges are approximately the same. This statement is false.

Step 3: Analyze "The female dog data is best represented by the median."

When data is skewed, the median is a better measure of central tendency than the mean because the mean is affected by extreme values. Since the female dog's data is skewed (from Step 1), the median is a good representative of the data. This statement is true.

Step 4: Analyze "The female dog data is less skewed than the male dog data."

Looking at the box - and - whisker plots, the male dog's box seems more symmetric (the median is closer to the center of the box, and the whiskers are more balanced in length) compared to the female dog's box. So, the female dog's data is more skewed, not less skewed, than the male dog's data. This statement is false.

Answer:

• The female dog graph is skewed.
• The female dog data is best represented by the median.