Question

In a class of 100 students the mean marks obtained in a certain subject is 30 and in another class of 50 students, the mean marks obtained in the same subject is 60. The mean marks obtained by the students of two classes taken together is
A) 40
B) 45
C) 48
D) 50

Answer 1

Hint: First find the total marks of 100 students whose mean marks are 30 by the mean formula $\bar x = \dfrac{{\sum {{x_i}} }}{n}$. After that find the total marks of 50 students whose mean marks are 60 by the same mean formula. Then add both marks and divide by the sum of the number of students from both classes to get the mean marks of the students of two classes together.

Complete step-by-step solution:
Let total marks of 100 students be a and total marks of 50 students are b.
We know that the general formula to find the mean value is,
Mean $ = \dfrac{{\sum {{x_i}} }}{n}$
The mean marks of 100 students in a class are 30.
Substitute the values in the mean formula to get the total marks,
$ \Rightarrow 30 = \dfrac{a}{{100}}$
Cross multiply the terms,
$ \Rightarrow a = 3000$...............….. (1)
The mean marks of 50 students in another class are 60.
Substitute the values in the mean formula to get the total marks,
$ \Rightarrow 60 = \dfrac{b}{{50}}$
Cross multiply the terms,
$ \Rightarrow b = 3000$.................….. (2)
Now add both equations to get the total marks of both classes,
$ \Rightarrow a + b = 3000 + 3000$
Add the terms,
$ \Rightarrow a + b = 6000$
Now, substitute the values in the mean formula to get the mean marks of students of both classes,
$ \Rightarrow \bar x = \dfrac{{6000}}{{150}}$
Divide numerator by the denominator to get the mean marks,
$\therefore \bar x = 40$

Hence, option (A) is correct.

Note: We need to know that the mean is adding the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words, it is the sum divided by the count. Do not forget any marks by adding up the values.