Question

The mean score of 7 boys and 16 girls is 49. If the scores of the boys are 42,85,47,29,58,54and 72, find the mean score of the girls

Answer 1

`\bar x_(girls) = 46.25`

Explanation:

Given

`Boys = 7\\Girls = 16`

`\bar x = 49`

Required

Mean of girls

The mean of the boys and girls is calculated as:

`\bar x = (\sum x)/(n)`

This gives:

`\bar x = (\sum(boys) + \sum(girls))/(boys + girls)`

So, we have:

`49= (42+85+47+29+58+54+ 72 + \sum(girls))/(7 + 16)`

`49= (387 + \sum(girls))/(23)`

Cross multiply

`23 * 49=387 + \sum(girls)`

`1127=387 + \sum(girls)`

Subtract by 387

`1127-387 = \sum(girls)`

`740= \sum(girls)`

`\sum(girls) = 740`

The mean of girls is:

`\bar x_(girls) = (\sum(girls))/(girls)`

`\bar x_(girls) = (740)/(16)`

`\bar x_(girls) = 46.25`