Question

The table below shows the drop-out rates, in percentage, at the Primary level (Classes I-V), the Elementary level (Classes I-VIII), and the Secondary level (Classes I-X) in India, separately for boys, girls, and the total, for the years 1996-97 to 2004-05.

Gender bias is defined as the disproportion between the drop-out rate of boys and the drop-out rate of girls, at a given level.

Suppose that every year, 7,000 students enter Class I, of which 45% are boys. What was the average number, as a whole number, of girls who stayed on in the education system beyond elementary classes, over the years 1996-97 to 2004-05?

• A. 1475
• B. 1573
• C. 1743
• D. 1673

Hint:

Girls entering each year are 55% of 7,000, that is 3,850; multiply this by (1 minus that year's elementary drop-out rate for girls) for each of the nine years, then average the nine results.

Answer 1

The Correct Option is D

Instead of computing nine separate retained-girl counts and then averaging them, it is quicker to average the nine drop-out rates first and apply the fixed number of girls only once.

1. Average the elementary drop-out rate for girls across the nine years: the nine values are $59.5, 59.3, 59.2, 58.0, 57.7, 56.9, 53.5, 52.9, 51.2$. Adding these gives $508.2$, so the average rate is $508.2/9 \approx 56.5$ percent.
2. Convert this into a retention rate: if $56.5$ percent of girls drop out on average, then about $100-56.5=43.5$ percent stay on beyond elementary classes.
3. Apply this to the fixed number of girls entering each year: girls entering are $55$ percent of $7000$, that is $3850$. So the average number who stay on is $3850 \times 0.435 \approx 1675$.

This estimate of about $1675$ lands almost exactly where the year by year method does, and among the four options it sits closest to $1673$, not to $1475$, $1573$, or $1743$.

Let's summarize:

• Averaging the nine drop-out rates first and then applying the fixed girl count once gives nearly the same answer as averaging nine separate yearly counts.
• Both routes point to the same option, about 1673 girls.

So the average number of girls staying on beyond elementary classes is closest to 1673.