Question

The number of students in four classes A, B, C, D and their respective mean marks obtained by each of the class are given below:
Class A Class B Class C Class D
Number of students 10 40 30 20
Arithmetic mean 20 30 50 15
The combined mean of the marks of four classes together will be:
(A) 32
(B) 50
(C) 20
(D) 15

Answer 1

Answer:

$Combined\:mean,\bar{x}=32$

option (A) is correct

Step-by-step explanation:

Formula used:

$Combined\:mean,\bar{x}=\frac{n_1\:\bar{x_1}+n_2\:\bar{x_2}+n_3\:\bar{x_3}+n_4\:\bar{x_4}}{n_1+n_2+n_3+n_4}$

Given:

$n_1=10$

$n_2=40$

$n_3=30$

$n_4=20$

$\bar{x_1}=20$

$\bar{x_2}=30$

$\bar{x_3}=50$

$\bar{x_4}=15$

$Combined\:mean,\bar{x}=\frac{n_1\:\bar{x_1}+n_2\:\bar{x_2}+n_3\:\bar{x_3}+n_4\:\bar{x_4}}{n_1+n_2+n_3+n_4}$

$Combined\:mean,\bar{x}=\frac{(10)(20)+(40)(30)+(30)(50)+(20)(15)}{10+40+30+20}$

$Combined\:mean,\bar{x}=\frac{200+1200+1500+300}{100}$

$Combined\:mean,\bar{x}=\frac{3200}{100}$

$Combined\:mean,\bar{x}=32$