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.

Explanation:

Step1: Analyze skewness

By observing the box - and - whisker plots, the female dog graph is more symmetric, while the male dog graph is skewed. So the statement "The female dog graph is skewed" is false and "The female dog data is less skewed than the male dog data" is true.

Step2: Calculate range

The range is the difference between the maximum and minimum values. For male dogs, assume minimum is around 40 and maximum is around 100, range is approximately \(100 - 40=60\). For female dogs, assume minimum is around 40 and maximum is around 95, range is approximately \(95 - 40 = 55\). So the statement "The range for female dogs is much larger than the range for male dogs" is false.

Step3: Consider data representation

Since the female dog data is more symmetric, the mean and median are close, but in general for symmetric data, the mean can also be a good representation. However, when data has outliers (which is not obvious here but still possible), the median is a more robust measure. So "The female dog data is best represented by the median" is a reasonable statement as median is less affected by potential outliers.

Answer:

The female dog data is best represented by the median.
The female dog data is less skewed than the male dog data.