Math, asked by varunbonthala2005, 2 months ago

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

Answered by amitnrw
0

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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