Question

The histogram shows the duration, in minutes, of movies in theaters.

What relationship between the median and mean is shown by the histogram?

The mean is less than the median.
The median is less than the mean.
The mean is equal to the median.
The median and mean cannot be compared from a histogram.

Answer 1

Option B) The median is less than the mean.

Explanation:

We are given the following in the question:

A histogram showing the duration, in minutes, of movies in theaters.

• If we observe the shape of the histogram, more values of the histogram lies on the right side, the tail of the distribution is longer on the right hand side than on the left hand side
• Hence, the histogram is skewed right.
• The histogram is not normal and shows skewness.
• It is a right skewed histogram or positively skewed.
• Now, for a positively skewed data the mean is greater than the median since more values lies on right side and have a greater value thus the mean increases.
• 
  `\text{Mean} > \text{Median}`
• The relationship shown by the histogram between mean and median is that median is less than the mean

Answer 2

The correct answer is:

The median is less than the mean.

Explanation:

This histogram is skewed right; the data "peaks" further to the left than the center.

If a histogram is skewed right, the mean is greater than the median.

This is because skewed-right data have a few large values that increase the mean but do not affect where the exact middle of the data is.