Candidates of four schools appear in a mathematics test. The data were as follows:
Schools | Number of candidates | Average score |
I | 60 | 75 |
II | 48 | 80 |
III | Not available | 55 |
IV | 40 | 50 |
If the average score of the candidates of all the four schools is 66
Given:
The average score of the candidates of all the four schools is 66.
To do:
We have to find the number of candidates that appeared from school III.
Solution:
Let the number of candidates that appeared from school III be $p$.
Therefore,
Schools | No.of candidates ($f$) | Average Score ($x$) | Total Score ($f \times\ x$) |
II | 60 | 75 | 4500 |
II | 48 | 80 | 3840 |
III | $p$ | 55 | $55p$ |
IV | 40 | 50 | 2000 |
Total | $148+p$ | | $10340+55p$ |
We know that,
Mean$=\frac{\sum fx}{\sum f}$
Therefore,
Mean $66=\frac{10340+55p}{148+p}$
$66(148+p)=10340+55p$
$9768+66p=10340+55p$
$66p-55p=10340-9768$
$11p=572$
$p=\frac{572}{11}$
$p=52$
The number of candidates that appeared from school III is $52$.
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