Variance (Deviation)

In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable’s mean.

• Larger deviation means the distribution spread wider.
• Smaller deviation means the distribution stick closer.

Standard Deviation

Also called Standard Variance.

Refer to Khan academy review: Calculating standard deviation step by step

(▲ where ∑ means "sum of", x is each value in the data set, μ(mu) is the mean of the data set, and N is the amount of data points in the population.)

Steps:

• Find the mean.
• Find the distance from each value to the mean.
• Find the average of all squared distances.
• Find the root of the average.

Example

Solve:

• By eyeballing, for Freshmen most of the data are not clustered around the mean.
• But for Seniors, most of the data points are clustered around the centre.
• So Freshmen has greater Standard Deviation.
• The seniors’ data resembles a Normal Distribution, in which the Standard Deviation is a good measure for the spread.