# Sample variance

Sample variance is a statistical measure that represents the degree of variability or dispersion of a set of data points from their mean or average value. It is calculated by taking the average of the squared differences of each data point from the mean.

Here is the formula for sample variance:

s^2 = Σ(x – x̄)^2 / (n – 1)

Where:

• s^2 is the sample variance
• x is each data point
• x̄ is the mean or average value of the data set
• n is the number of data points in the sample

To calculate the sample variance, follow these steps:

1. Calculate the mean of the data set by adding up all the data points and dividing by the number of data points.
2. Subtract the mean from each data point.
3. Square each difference.
4. Add up the squared differences.
5. Divide the sum of squared differences by (n – 1), where n is the number of data points in the sample.

For example, let’s say we have the following data set:

{10, 15, 12, 18, 20}

To calculate the sample variance:

1. Calculate the mean: x̄ = (10 + 15 + 12 + 18 + 20) / 5 = 15
2. Subtract the mean from each data point: (10 – 15) = -5, (15 – 15) = 0, (12 – 15) = -3, (18 – 15) = 3, (20 – 15) = 5
3. Square each difference: (-5)^2 = 25, 0^2 = 0, (-3)^2 = 9, 3^2 = 9, 5^2 = 25
4. Add up the squared differences: 25 + 0 + 9 + 9 + 25 = 68
5. Divide the sum by (n – 1): s^2 = 68 / (5 – 1) = 17

Therefore, the sample variance of this data set is 17.