How Would You Estimate The Number Of Indian Teenagers

We often think of India as a developing country, and expect that there is a significantly larger group of really young children, which implies that the lower quartile is much less than half of the median. However, given the data that the median age is 24 and the lower quarter is $\frac{24}{2} =12$ , that hypothesis is now suspect .

Instead, what is likely is that the mode occurs in the range 10-15 (around 12), with fewer children in ages below 10 or above 15. As we are concerned with those aged 13-19, we can still make the reasonable assumption that on average , there are $\frac{1210}{2} \div 25$ million in each age group. As such, this gives us $\frac{ 1210} { 2} \times \frac{7}{25} \approx 170$ million.

In fact, India's population structure has began to change in the recent 5-10 years. The following is a graph of age against population size, based on data available from the government census.

Imager

You will notice that there number of young children is on the decline, and that the mode occurs around ages 10-15, like we predicted above.

What do you think is the reason for some of the really long red bars?

You are given Total Population = 1.210 billion.

The median tells you the value at which half the population is larger and half is smaller. This means half the population is under or aged 24. So approximately 605 million are 0 - 24 years old.

${1.210 \over 2} = .605 \text{ billion} = 605 \text{ million}$

The lower quartile tells you the value at which half of the lower half of the total population is larger and half is smaller. In other words, its sort of like the median of the lower half of the total population. This means approximately 302.5 million are aged 12 - 24.

${605 \over 2} = 302.5 \text{ million}$

We want to find the part of that 302.5 million that are aged 13 -19. Since this is an estimate, we can assume there is an equal proportion of people in each age group. For our purposes, there are 12 age groups, since only half of the people in the age group 12 or 24 are within our 302.5 million. This means approximately 25.2 million are in each age group.

${302.5 \over 2} \approx 25.2 \text{ million}$

We are interested in the age groups 13-19, which there is 7 group. So we can just multiply 25.2 by 7 to get the total estimated population that are 13-19 years old. We get approximately 176.4 million aged 13-19.

$25.2 \cdot 7 = 176.4 \text{ million}$

Our closest option is 170 million, so that is our answer.