Q.The variance of 19, 21, 23, 25 and 27 is 8. The variance of 14, 16, 18, 20 & 22 is: A) Greater than 8 B) 8 C) Less than 8 D) 8 − 5 = 3

Variance and standard deviation behave in a specific, useful way when data is shifted or rescaled, and this property is used to simplify hand calculations, especially for grouped data with a large class mark. If a new variable is formed purely by shifting the origin, d = x − A (subtracting a constant A, often the mid-value of a central class), variance and standard deviation are unaffected: σ²_d = σ²_x and σ_d = σ_x — spread does not change just because every value is shifted by the same amount. However, if the data are also rescaled, u = (x − A)/h, where h is the class width (or, for ungrouped data, the common gap between consecutive values), then variance and standard deviation DO change with the scale: σ_x = h·σ_u and σ²_x = h²·σ²_u. In practice this means the mean …