Mean and median height: An association of U. S. dog breeders reported in a recent year that the mean height for their adult dogs was 22.0 inches, and the median was 15.9 inches. Of a histogram were constructed for the heights of all adult dogs in the U. S., would you expect it to be skewed to the right, skewed to the left, or approximately symmetric?

Question

Kaiden Lloyd

Mathematics

30 April, 21:20

Mean and median height: An association of U. S. dog breeders reported in a recent year that the mean height for their adult dogs was 22.0 inches, and the median was 15.9 inches. Of a histogram were constructed for the heights of all adult dogs in the U. S., would you expect it to be skewed to the right, skewed to the left, or approximately symmetric?

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Kristina Villarreal · Answer 1

We should expect the histogram to be skewed to the right.

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

The mean is the average of all the values in the set.

Median, mean and skewness of the histogram:

If the mean is greater than the median, the histogram has positive skewness, that is, it is skewed to the right.

If the mean is lesser than the median, the histogram has negative skewness, that is, it is skewed to the left.

If the mean and the median are equal, the histogram is approximately symmetric.

In this problem, we have that:

Mean = 22

Median = 15.9

So we should expect the histogram to be skewed to the right.