The data given below presents the number of households corresponding to the number of children residing there in.
What is the difference (correct up to two decimal places) between the mean and the median of the number of children?
Solution
mean of the number of children = $$\frac{total\ number\ of\ children}{number\ of\ households}$$
= $$\frac{8\times0+7\times1+3\times2+8\times3+4\times4}{8+7+3+8+4}$$
= $$\frac{0+7+6+24+16}{30}$$
= $$\frac{53}{30}$$
= 1.77
median of the number of children = $$\frac{\left(\frac{n}{2}\right)^{th}+\left(\frac{n}{2}+1\right)^{th}}{2}$$
= $$\frac{\left(\frac{30}{2}\right)^{th}+\left(\frac{30}{2}+1\right)^{th}}{2}$$
= $$\frac{15^{th}+\left(15+1\right)^{th}}{2}$$
= $$\frac{15^{th}+16^{th}}{2}$$= $$\frac{1+2}{2}$$
= $$\frac{3}{2}$$
= 1.5
Difference between the mean and the median of the number of children = 1.77-1.5
= 0.27
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