Consider the following data: | | Average marks in English | Average marks in Hindi | |---|---|---| | Girls |…
Consider the following data:
| | Average marks in English | Average marks in Hindi |
|---|---|---|
| Girls | 9 | 8 |
| Boys | 8 | 7 |
| Overall average marks | 8.8 | x |
What is the value of $x$ in the above table?
7.8
7.6
7.4
7.2
Solution
Overall English average 8.8 lies between boys' 8 and girls' 9. By weighted average: if fraction of girls is $g$, then $9g + 8(1-g) = 8.8$, giving $g = 0.8$ (girls) and boys $= 0.2$. For Hindi: $x = 8(0.8) + 7(0.2) = 6.4 + 1.4 = 7.8$.