Let the mean and variance of 12 observations be 
and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is 
, where m and n are coprime, then m + n are coprime, then m + n is equal to
Text Solution
Verified by ExpertsD
Given,
The mean and variance of 12 observations be 
and 4 respectively,
So, mean will be,
x l + x 2 ......+ x n + 19 = 54
Now removing the observation 9 & 10 and adding the observation 7 & 14,
So, the new total sum of the observation will be,
x 1 + x 2 +......+ x 12 + 7 + 14 = 54 - 19 + 7 + 14
Now new mean will be,
Now using the formula of the variance we get,
Now removing 9 2 & 10 2 and adding 7 2 & 14 2 we get,
New variance 
Now on comparing with 
we get,
m = 281 and n = 36
m + n = 317
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems