Question

National Park rangers keep data on the bears that inhabit their park. Here is a histogram of the weights of bears measured in a recent year:

Which of the following statements is correct?

a. The median will lie in the interval $(140,180)$, and the mean will lie in the interval$(180,220)$.

b. The median will lie in the interval$(140,180)$, and the mean will lie in the interval $(260,300).$

c. The median will lie in the interval$(100,140),$ and the mean will lie in the interval $(180,220)$.

d. The mean will lie in the interval $(140,180),$and the median will lie in the interval $(260,300).$

e. The mean will lie in the interval $(100,140),$ and the median will lie in the interval $(180,220)$.

Short answer

The correct option is:

a.The median will lie in the interval $(140,180)$, and the mean will lie in the interval $(180,220)$.

Step-by-step solution

 Step 1: Given information 

We have to tell about weights of bears measured in a recent year.

Explanation 

Because the greatest bars in the histogram are to the left of the histogram and a tail of lower bars are to the right, the provided distribution is substantially skewed to the right.

The median is generally at the top of the histogram, which is the bar with the midpoint of $160$ pounds, hence the interval $(140,180)(140,180)$ is the most likely to include the median.

Because the mean is larger than the median but not by a significant amount, we expect the mean to be located at the bar to the right of the median's bar. We expect the mean to be in the range $(180,220)$ because this is the bar with the midpoint$200.(180,220).$