1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 xi and the unit of their mean are different that of variance. Since, variance involves sum of squares of (x- barx)

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Q. 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 $(x-\bar{x})$

Statistics

Solution:

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.