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 29.4 inches, and the median was 28.5 inches. If 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

Mathematics

Kade Adkins

21 August, 15:55

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 29.4 inches, and the median was 28.5 inches. If 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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Answers (1)

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Marisol Bailey · Answer 1

Skewed to the left.

Step-by-step explanation:

Relationship between the mean and the median:

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

The median is the one separating the lower 50% values of a set from the upper 50% of the values.

If the mean and the median are the same, the distribution is symmetric. That is, 50% of the values are above the mean, and 50% are below.

If the mean is higher than the median, the distribution is skewed to the left. Which means that a percentage higher than 50% of the values are below the mean, and a percentage lower than 50% of the values are above the mean.

If the mean is lower than the median, the distribution is skewed to the right. Which means that a percentage higher than 50% of the values are above the mean, and a percentage lower than 50% of the values are below the mean.

In this problem, we have that:

Mean = 29.4 inches

Median = 28.5 inches

Mean higher than the median. Which means that the histogram is skewed to the left.