the mean and variance are 15 and 15 respectively if one of the observation 15 is deleted and two new observation of resulting data is
Answers
Given : the mean and variance are 15 and 15 respectively
if one of the observation 15 is deleted
To Find : mean and variance of resulting data
Solution:
Let say there are N observations
=> Total = 15N
as Mean = 15
New Mean = (15N - 15) / ( N - 1) = 15(N -1)/(N - 1) = 15
No change in Mean
new Mean = 15
Variance = ∑(x - mean)² /N
=> 15 = ∑(x - mean)² /N
=> 15N = ∑(x - mean)²
for New Variance ∑(x - mean)² = 15N as term removed is ( 15 - 15)² = 0
Hence no change in ∑(x - mean)²
But term are now N - 1
Hence New Variance = 15N /(N - 1)
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