Question

The distribution of sample means calculated using samples of size 16 has a mean of 100 and a standard error of 2.25. What is the variance of the original distribution?

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**Answer:**

Variance of the sample means is given by

=>
_{x}^{2} =
^{2}/N

=>
^{2} =
_{x}^{2} * N

==> Population variance = Standard devation^2/N

Std dev = std. error*sqrt(n)

= 2.25*16 = 36

=> Population variance = 36^2*16

= 20736

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