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

Answer:

$\bar x_{girls} = 46.25$

Step-by-step explanation:

Given

$Boys = 7\\Girls = 16$

$\bar x = 49$

Required

Mean of girls

The mean of the boys and girls is calculated as:

$\bar x = \frac{\sum x}{n}$

This gives:

$\bar x = \frac{\sum(boys) + \sum(girls)}{boys + girls}$

So, we have:

$49= \frac{42+85+47+29+58+54+ 72 + \sum(girls)}{7 + 16}$

$49= \frac{387 + \sum(girls)}{23}$

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:

$\bar x_{girls} = \frac{\sum(girls)}{girls}$

$\bar x_{girls} = \frac{740}{16}$

$\bar x_{girls} = 46.25$