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# The variance of 20 observations is 5. If each observation is multiplied by 2, then find the new variance of the resulting observations.

Latika Leekha
6 years ago
Hello student,
Let the given observations be x1, x2, …. x20. and xM be their mean.
Given that n = 20 and variance is 5.
So, 

If each observation is multiplied by 2, then the new observations are yi = 2xi, i = 1, 2, … 20.
So, xi = yi/2.
Hence, 

= 2. 1/20 . xM
This gives us xM = ½ yM
Substituting the values of xi and xM in (1) we have



Hence, the variance of the resulting observations is = 1/20 . 400
= 20.
= 22.5
ankit singh
8 months ago

## If each observation is multiplied by 2, then mean(μ) will get doubled.

Now, variance =σ2=n(Xμ)2
Now here both X and μ will be doubled, so the variance will become four times.
Thus, the new variance will be 4 times the older variance which is 4×5=20.