Variance is independent of change of :

In statistics, the origin and scale of the term are related to the diagrammatic presentation of statistical data.

• Change of origin means some value has been added or subtracted to the value of the origin.
• Change of scale in statistics means that there is some value multiplied by the observations.

Key Points

• Variance is independent of change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when (x₁ -μ)² is calculated, it remains unaffected.
• For example x₁ + 5, x₂ + 5 Xn+5 than mean and x, both will change in the same manner so while we calculate (x₁ -μ)² it won't change.
• But, change of scale alters all values unevenly, and hence, variance changes.
• For example 2x₁, 2x2 also change. 2x than mean and x, both will change so variance also changes.

Thus, it is concluded that variance is independent of change of origin only.