Question

Which of the following defines mean deviation?

• A. Mean of deviations of observations from central value.
• B. Mean of absolute deviations of observations from central value.
• C. Mean of the observations in the data set
• D. Mean of deviations about most occurring value

Answer 1

The correct option is B

Mean of absolute deviations of observations from central value.

Given n observations $x_1,x_2......x_n$ and their central tendency a
Absolute deviations of observations about a will be

$|$ $x_1$ - a $|$, $|$ $x_2$ - a $|$, $|$ $x_3$ - a $|$....$|$ $x_n$ - a $|$

$\therefore$ Mean of absolute deviations = $\frac{|x_1-a|+|x_2-a|+....+|x_n-a|}{n}$

= $\frac{{\sum }_{i=1}^n|x_i-a|}{n}$

$\therefore$ MD(a) = $\frac{{\sum }_{i=1}^n|x_i-a|}{n}$

If the absolute value is not taken the actual deviations may cancel out each other which won't serve the purpose we need.
The central value can be calculated in several ways and need not be the most recurring value all the time.

$\therefore$ Option b