Question

There are 45 students in a class out of which 15 are girls. The average weight of 15 girls is 45kg and the 30 boys 52 kg. Find the average weight of whole class​

Answer 1

Given,

Number of Students in the class = 45

Number of girls in the class = 15

Then, the boys = 45 - 15 = 30

Average weight of 15 girls = 45kg

Total sum of the girls weight = x

Mean = Sum of all observations / Number of observations

45 = x/15

x = 45 × 15

x = 675

The total sum of the girls weight = 675

Average weight of boys = 52

Total sum of the boys weight = y

Mean = Sum of all observations / Number of observations

52 = y/30

y = 52 × 30

y = 1560

The total sum of boys weight = 1560

Sum of weights of total class = 675 + 1560 = 2235

Mean of the whole class = 2235/45 = 49.6

Therefore, the average weight of the class = 49.6

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Average weight of the students in the Class is 49.6 kg.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Total Students = 45 Students

Girls in the class = 15 girls

Average weight of girls = 45 kg.

Boys in the class = 45 - 15 = 30

Average weight of boys = 52 kg.

To find :

The average weight of whole class.

Solution :

First we need to find the sum of the weight of girls in the girls.

Consider the total weight of girls as x

★ We know that :

$\tt{Average = \dfrac{Sum \: of \: Observations}{No. \: of \: Observations}}$

As We are given with the mean (Average). Equation Formed would be :

$\tt{\implies} \: 45 = \dfrac{x}{15}$

$\tt{\implies} \: 45 \times 15 = x$

$\tt{\implies} \: x = 675$

Total weight of girls = 675 kg.

Find the total weight of Boys.

★ We know that :

$\tt{Average = \dfrac{Sum \: of \: Observations}{No. \: of \: Observations}}$

Consider the total weight of Boys as y

$\tt{\implies} \: 52 = \dfrac{x}{30}$

$\tt{\implies} \: 52 \times 30 = x$

$\tt{\implies} \: x = 1560$

Total weight of Boys = 1560 kg.

$\rule{300}{1}$

Average of the weight of the students from the whole class.

Find the average :

$\tt{\implies} \: Average = \dfrac{1560 + 675}{45}$

$\tt{\implies} \: \dfrac{2235}{45}$

$\tt{\implies} \: 49.6$

$\therefore$ The Average weight of the students in the Class is 49.6 kg.