Question

Find the mean of 30 memebers given mean is 12 and the mean of remaining 20 is 9

Answer 1

Answer:

10

Note:

Sum of observations

★ Mean = --------------------------------

No. of observations

Solution:

It is given that ;

Among 30 members , the mean of first 10 members is 12 and the mean of remaining 20 members is 9 .

Here,

We need to find the mean of 30 members.

Thus,

Let the 30 members be ;

m1 , m2 , m3 , ....... , m30

Now,

According to the question , the mean of first 10 members is 12 .

Thus,

=> ( Sum of first 10 members ) / 10 = 12

=> (m1 + m2 + m3 +....+ m10) / 10 = 12

=> m1 + m2 + m3 +....+ m10 = 12×10

=> m1 + m2 + m3 +....+ m10 = 120 --------(1)

Also,

The mean of remaining 20 members is 9.

Thus,

=> ( Sum of next 200 members ) / 20 = 9

=> (m11 + m12 + m13 +....+ m30) / 20 = 9

=> m11 + m12 + m13 +....+ m30 = 19×20

=> m11 + m12 + m13 +....+ m30 = 180 ------(2)

Now,

The mean of all the 30 members will be given as ; (Sum of all 30 members) / 30

= [m1 + m2 + m3 +....+ m30] / 30

= [(m1 + m2 + m3 + ...+ m10)

+ (m11 + m12 + m13 + ... + m30 ] / 30

= [ 120 + 180 ] / 30 { using eq-(1) and (2) }

= 300 / 30

= 10

Hence,

The required mean of 30 members is 10 .