Question

Birthrates in Africa One of the important factors in determining population growth rates is the birthrate per 1000 individuals in a population. The dotplot shows the birthrates per 1000 individuals (rounded to the nearest whole number) for 54 African nations.

(a) Find the median.

(b) Without doing any calculations, explain how the mean and median compare.

Short answer

Part (a) 37.5 birth per 1000 individuals.

Part (b) The median is higher than the mean, but the mean is lower.

Step-by-step solution

Part (a) Step 1. Given information.

The given data is shown below:

The data values are:

12, 17, 18, 21, 23, 23, 23, 24, 25, 25, 25, 26, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 36, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 40, 40, 41, 41, 41, 43, 43, 43, 43, 44, 45, 45, 46, 46, 47, 53

Part (a) Step 1. Find the median.

As we know that median is the middle value of a data set. As the given set is even, the median will be the middle values (27th and 28th) of this sorted data:

$$\begin{gathered} M=\frac{37+38}{2} \\ =\frac{75}{2} \\ =37.5 \end{gathered}$$

Therefore, the median is 37.5 birth per 1000 individuals.

Part (b) Step 1. Compare the mean and median without doing any calculations.

We can observe that most of the values in the dot-plot are to the right, with a tail of more rare (small) values to the left, the distribution is skewed to the left.

The mean is lower than the median in a left-skewed distribution because the mean is influenced more by the abnormally tiny data values in the data set.