Question

A class has 25 students of which 10 are boys (you may assume that the other 15 are girls). The class average (mean) height is x metres and the mean height for boys is xb metres. The mean height for girls xg is

Answer 1

average height of class = (15*b + 20*g)/(15+20) where b is average height of boys and g is average height of girls.

average height of class = (15*b + 20*g)/(15+20) where b is average height of boys and g is average height of girls.

So 1.5 = (15b + 20*1.45)/35

Multiply both sides by 35

35*1.5 = 15b + 20*1.45

Subtract 20*1.45 from both sides

35*1.5 - 20*1.45 = 15b

Divide both sides by 15

b = (35*1.5 - 20*1.45)/15

or the average height of the boys is approximately 1.57m

Answer 2

The mean height for girls is

The mean height for girls is$\frac{25 - 10y}{15}$

Given:

A class has 25 students of which 10 are boys (you may assume that the other 15 are girls). The class average (mean) height is x meters and the mean height for boys is xb meters.

To Find:

The mean height for girls.

Solution:

To find the mean height of girls we will follow the following steps:

As we know,

Mean is the sum of all the numbers divided by the total numbers.

According to the question:

Total students = 25

Total boys xb = 10

Total girls xg = 15

The mean of class height is x meters.

So,

$mean = \frac{total \: sum \: of \: height}{total \: students}$

$x = \frac{sum \: of \: height \: of \: boys + sum \: of \: height \: of \: girls}{25}$

$sum \: of \: height \: of \: boys + sum \: of \: height \: of \: girls = 25x$

Also,

Mean of the height of boys = y meters

$The \: mean \: height \: of \: boys= \frac{sum \: of \: height}{10}$

$y = \frac{sum \: of \: height}{10}$

$sum \: of \: height = 10y$

As proved above:

$sum \: of \: height \: of \: boys + sum \: of \: height \: of \: girls = 25x$

$10y + sum \: of \: height \: of \: girls = 25x$

$sum \: of \: height \: of \: girls = 25x - 10y$

Now,

The mean height of girls =

$\frac{sum \: of \: height \: of \: girls}{total \: girls} = \frac{25x - 10y}{15}$

Henceforth, The mean height for girls is $\frac{25 - 10y}{15}$

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