Question

airthmatic mean of weight of 100 boys is 50 kg and the arithmetic mean of 50 girls is 45kg calculated the arithmetic mean of combined group of boys and girls.

Answer 1

$combined \: mean \: = \frac{50 \times 100 + 45 \times 50}{100 + 50} \\ = \frac{5000 +2250 }{150 } \\ = \frac{7250}{150} \\ = 48.33kg$

Answer 2

Given:

The arithmetic mean of the weight of 100 boys is 50 kg and the arithmetic mean of 50 girls is 45kg.

To find:

The arithmetic mean of the combined group of boys and girls.

Solution:

First of all, we should know that the arithmetic mean of 'n' observations is equal to the sum of all 'n' observations divided by the total number of observations i.e. n.

This means

$arithmetic \: mean = \frac{sum \: of \: n \: observations}{n}$

So,

as given, we have,

The arithmetic mean of the weight of 100 boys is 50 kg.

So, the sum of the weight of 100 boys

$= 50 \times 100$

$= 5000 \: kg$

Also,

the arithmetic mean of 50 girls is 45kg.

So, the sum of the weight of 50 girls

$= 45 \times 50$

$= 2250 \: kg$

So,

the arithmetic mean of a combined group of 100 boys and 50 girls

$= \frac{5000 + 2250}{100 + 50}$

$= \frac{7250}{150}$

$= 48.33\: Kg$

Hence, the arithmetic mean of 100 boys and 50 girls is 48.33 Kg.