Variance and Standard Deviation

The variance and standard deviation are two very popular measures of variation. Their formulations are categorized into whether to evaluate from a population or from a sample.

Population variance
The average of the population’s squared deviations from the mean

σ² = Σ[f_i( x_i - μ)²]/ Σf_i

Where:
f_i - the frequency of the ith item;
x_i - the value of the ith item or class mark;
μ- the population arithmetic mean.

Population standard deviation σ is defined as σ = σ^1/2

Sample variance
s² = Σ[f_i( x_i - x_a)²]/( Σ f_i – 1) = Σ[f_i( x_i - x_a)²]/(n – 1)

Where: f_i = n

Sample standard deviation is the square root of sample variance.


My tips:

• The formula of variance and standard deviation are complicated. Better to use calculator to input the data and get the answer directly.
• Be remembered that the standard deviation is the square root of varaince.