Question

If everyone in a population has the same score, what is the value of the standard deviation for those scores?

Answer 1

The formula for population standard deviation is,

Where X_i are scores in population.

If all scores are same then the mean of all score is, X_i

That is, if we take population of size 5 and scores are same as follows, 2, 2, 2, 2, 2

then mean = ( 2 + 2 + 2 + 2 + 2)/5 = 10/5 = 2

and standard deviation is,

Hence, if everyone in a population has the same score, then the value of the standard deviation for those scores is zero.