Question

Statement I In order to find the dispersion of values of $x$ from mean $\bar{x}$, we take absolute measure of dispersion.
Statement II Sum of the deviations from mean $(\bar{x})$ is zero.

• 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)

The deviation of an observation $x$ from a fixed value ' $a$ ' is the difference $(x-a)$. In order to find the dispersion of values of $x$ from a central value $a$, we find the deviations about $a$. An absolute measure of dispersion is the mean of these deviations.
To find the mean, we must obtain the sum of the deviations. But, we know that a measure of central tendency lies between the maximum and the minimum values of the set of observations.
Therefore, some of the deviations will be negative and some positive. Thus, the sum of deviations may vanish. Moreover, the sum of the deviations from mean $\bar{x})$ is zero. Also,
Mean of deviations $=\frac{\text{ Sum of deviations }}{\text{ Number of observations }}=\frac{0}{n}=0$
Thus, finding the mean of deviations about mean is not of any use for us, as far as the measure of dispersion is concerned.