Question

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. done

Explanation:

Step1: Analyze skewness

For skewness, in a box - plot, if the median is not in the center of the box and the whiskers are of unequal length, the data is skewed. The female dog graph (blue) has a median closer to the left of the box and a longer right - whisker, so it is skewed.

Step2: Analyze range

The range is calculated as \(R=\text{Max}-\text{Min}\). For male dogs (orange), assume \(Max\) and \(Min\) are the end - points of the whiskers. For female dogs (blue), assume \(Max\) and \(Min\) are the end - points of the whiskers. By visual inspection (since the scale is the same), the length of the whiskers (range) for male and female dogs seems to be approximately the same.

Step3: Analyze representation by median

When data is skewed, the median is a better measure of central tendency than the mean. Since the female dog data is skewed (from Step 1), the median is a better representation.

Step4: Compare skewness

The male dog graph (orange) has a more symmetric - looking box (median closer to the center of the box) compared to the female dog graph (blue). So the female dog data is more skewed than the male dog data.

Answer:

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