Question

Statement I The proper measure of dispersion about the mean of a set of observations i.e., standard deviation is expressed as positive square root of the variance.
Statement II The units of individual observations $x_i$ and the unit of their mean are different that of variance. Since, variance involves sum of squares of $(x-\bar{x})$

• A. Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I
• B. Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
• C. Statement I is true; Statement II is false
• D. Statement I is false; Statement II is true

Answer 1

Answer: (A)

In the calculation of variance, we find that the units of individual observations $x_i$ and the unit of their mean $\bar{x}$ are different from that of variance, since variance involves the sum of squares of $\left(x_i-\bar{x}\right)$. For this reason, the proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation.