The variance of 20 observations = 5.If each observation is multiplied by 5, then the new variance will be

Concept:

Multiplying every value by a constant:- however, will multiply the mean, median, quartiles, range, interquartile range, and standard deviation by that constant, and multiply the variance by the square of that constant.

Var X = \(\rm \sum (X_i\ -\ \overline X)^2\over N\)

Calculation:

Var X = \(\rm \sum (X_i\ -\ \overline X)^2\over 20\) = 5

New observations = 5X₁, 5X₂, ...,5X₂₀

New \(\rm \overline X ={5X_1\ +\ 5X_2\ +\ ...\ +\ 5X_{20}\over 20}\)

=  \(\rm 5\left({X_1\ +\ X_2\ +\ ...\ +\ X_{20}\over 20}\right)\)

= 5X_old

New Var X = \(\rm \sum (5X_i \ -\ 5\overline X)^2\over 20\)

= 25 × \(\rm \sum (X_i\ -\ \overline X)^2\over 20\)

= 25 × 5

= 125