Is it possible for the standard deviation of a set of data to be zero? Explain.

Question

 standard deviation 

Answer 1

The formula for the standard deviation is:

 

σ = [(1/N)SIGMA(x-μ)²]^1/2

 

where

σ is the standard deviation

SIGMA is the sum of all of the (x-μ)²

x is a data point in the data set

μ is the mean

N is the number of data points in the data set

 

For the standard deviation to be zero, then (x-μ)² must be zero for every x, which means that every data point equals the mean.