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