Question

The average marks of 50 students of a dássis 54. If 20 students of the class have average marks 60, find the average marks of the remaining 30 students.


please don't post irrelevant answers and don't know type​

Answer 1

Answer:

The average marks of the remaining 30 students is 50.

Step-by-step explanation:

Given :

The average marks of 50 students of a class is 54.

20 students of the class have average marks 60.

To find :

the average marks of the remaining 30 students.

Solution :

We know,

Average = Sum of observations/no.of observations

__________________

The average marks of 50 students of a class = 54

So,

Sum of the marks of 50 students/50 = 54

Sum of the marks of 50 students = 54 × 50

Sum of the marks of 50 students = 2700

Now,

20 students of the class have average marks of 60.

Sum of the marks of 20 students/20 = 60

Sum of the marks of 20 students = 60 × 20

Sum of the marks of 20 students = 1200

We've to find the average marks of the remaining 30 students.

Let the sum of the marks of remaining 30 students be 'x'

Sum of the marks of 50 students is equal to the sum of the marks of 20 students and that of the remaining 30 students.

2700 = 1200 + x

x = 2700 – 1200

x = 1500

Average marks of the remaining 30 students :

= Sum of the marks of 30 students/30

= 1500/30

= 50

Therefore, the average marks of the remaining 30 students is 50.

Answer 2

Solution!!

Average marks can also be called mean marks.

Mean marks of 20 students = 60

Mean marks of 30 students = x

Mean marks of 50 students (Combined mean) = 54

Using a formula:-

$\sf \bold{\overline{x}_{12}=\dfrac{N_{1}\overline{x}_{1}+N_{2}\overline{x}_{2}}{N_{1}+N_{2}}}$

Here,

$\sf \overline{x}$₁₂ is combined mean of 50 students.

N₁ represents 20 students (first group).

$\sf \overline{x}$₁ is the mean marks of 20 students.

N₂ represents 30 students (second group).

$\sf \overline{x}$₂ is the mean marks of 30 students.

$\sf 54=\dfrac{20(60)+30(x)}{20+30}$

54 × 50 = 1200 + 30x

2700 = 1200 + 30x

30x = 1500

x = 50

Hence, the mean/average marks of 30 students is 50.