Question

If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained:

• A. increases by \( k \)
• B. do not change
• C. is equal to \( k^2 \)
• D. is equal to \( 2k \)

Hint:

Adding or subtracting a constant to all observations does not affect the variance; it only shifts the data.

Answer 1

The Correct Option is B

The variance is not affected by the addition or subtraction of a constant value \( k \). It only depends on the spread of the data points. Therefore, the variance remains unchanged.