Question

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 ($180,200$).

Short answer

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

Step-by-step solution

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.

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 $(140,180)$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 $(180,220)$.

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 ($180,220$).