analysis how do you do this

Question

The National Center for Health Statistics sampled 5844 American women over the age of 20 and found that their median weight was 157.2 pounds. A histogram of the data set was skewed to the right. Which of the following is a possible value for the mean weight: 150 pounds, 155 pounds, or 160 pounds? Explain.

I have been practicing and am unsure what you do with this question.

Answer 1

Suppose we have a set of values like (1, 2, 3, 4, 5) with only one value or each number. The mean and median are both 3. Now suppose we take the same set and include a large number, giving us (1, 2, 3, 4, 5, 50). The median is 3.5 and the mean is 10.8, or to the right of the median.

We can extend this idea to your question. Right tailed (or skewed) distributions mean that there may be a high frequency of lower values but a long tail of lower frequency large values and this will always skew the mean to the right of the median since those large values greatly increase the mean (as it did in the example I just gave).

With respect to your problem, the only possible mean weight you were given that's larger than the median (157.2 lbs) is 160 which, since this is a right skewed distribution, is your answer.