The tutor indicates the formula for calculating population standard deviation versus that for sample standard deviation.

The population variance, σ², has calculation formula

σ²=Σ₁^N(x_i-μ)^2/N

where N is the total count of the population, while μ is the mean.

The population standard deviation is σ, the square root of the variance.

The sample variance, s², has formula

s²=Σ₁ⁿ(x_i–x)^2/(n-1)

where n is the number of measurements in the sample, while x is the sample mean.

Once again, the standard deviation is the square root of the variance. Therefore, the sample standard deviation is s.

Technically, using the formula for population variance and/or standard deviation is only correct when every measurement from the population is included. For instance, if a teacher is calculating the standard deviation of the heights of members of her class, and every student’s height is used, then σ can be calculated for that class using the formula for population standard deviation.

Let’s imagine, on the other hand, a high school of perhaps 700 students, where 30 students’ heights are randomly measured, then used to estimate the standard deviation of the heights of all 700 students. In this case, the sample standard deviation formula should be used, yielding s. The population standard deviation, σ, cannot be calculated from a sample. It can be estimated from a sample; that estimate is s.

I’ll be talking more about variance and standard deviation in future posts:)

Source:

Harnettt, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics. Don Mills: Addison-Wesley, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.