Question

use the shape of the distribution to compare the mean and median. are the mean and median equal? if not, which is greater? explain your reasoning. data set: 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 40, 41, 41, 42, 42, 42, 43, 43, 44, 44, 45, 46, 46, 47, 48, 48, 49, 50

Explanation:

Step1: Determine the distribution shape

The histogram appears to be skewed right. In a right - skewed distribution, the tail of the distribution extends to the right.

Step2: Recall mean and median relationship in skewed distributions

In a right - skewed distribution, the mean is pulled in the direction of the tail. The median is the middle value and is less affected by extreme values. So, the mean is greater than the median.

Step3: Answer the equality question

Since the distribution is right - skewed, the mean and median are not equal.

Answer:

The mean and median are not equal. In a right - skewed distribution (as the given histogram appears to be), the mean is greater than the median because the mean is influenced by the extreme values in the right - tail while the median is the middle value and is less affected by these extreme values.