A sample of n = 25 scores have M = 20 and s² = 9. What is the sample standard deviation? 

Solution:

Given, n = 25 scores which means that there are 25 samples having M = 20, which is the arithmetic mean(A.M) of these samples, and s² = 9 is the variance of these samples.

Standard deviation is the square root of the variance.

Therefore, s² = 9 ⇒ s = 3

(where, s denotes sample standard deviation, σ)

Also, Standard error of the sample S(E) = Sample standard variance/√number of samples

⇒ σ/√n = 3/5 = 0.6

A sample of n = 25 scores have M = 20 and s² = 9. What is the sample standard deviation?

Summary:

The sample standard deviation of a sample of n = 25 scores have M = 20 and s² = 9 is 3 and the Standard error of sample S(E) is 0.6.