 Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q. 21

Expert-verified Found in: Page 669 ### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339 # National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of $143$ bears measured in a recent year. Which statement below 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 ($180,200$).

The correct statement is that the median will lie in the interval $\left(140,180\right)$ and the mean will lie in the interval $\left(180,220\right)$ i.e., correct option is (a).

See the step by step solution

## Step 1: Given Information

We are given with the histogram of the weights of $143$ bears measured in a recent year and we have to find out the mean and median interval.

## Step 2: Explanation

Now, as we know that in this histogram the distribution is skewed towards right because the lowest bars in the histogram are towards right and A right skewed distribution has the property that mean is larger than median.

So, in this median lies in the interval of highest bars and that is why $\left(140,180\right)$ will contain the median.

As the mean is larger than median thus it should be right to the median and this is the bar which have a mid point at $200$ and thus we can expect mean in $\left(180,220\right)$.

Hence, the correct statement is option (a) i.e., The median will lie in the interval ($140,180$), and the mean will lie in the interval ($180,220$). ### Want to see more solutions like these? 