# Mean Deviation Formula

The mean deviation also known as the mean absolute deviation is defined as the mean of the absolute deviations of the observations from the suitable average which may be the arithmetic mean, the median or the mode.

The formula to calculate Mean deviation is as stated below:

$\large Mean\;Deviation\;from\;Mean=\frac{\sum \left |X-\overline{X}\right|}{N}$

$\large Mean\;Deviation\;from\;Median=\frac{\sum \left |X-M\right|}{N}$

Here,
$\sum$, represents the summation.
X, represents the observation.
$\overline{X}$, represents the mean.
N represents the number of observation.

For frequency distribution, the mean deviation is given by

$\large M.D=\frac{\sum f \left | X-\overline{X} \right |}{\sum f}$

When the mean deviation is calculated about the median, the formula becomes

$\large M.D (about\;median)=\frac{\sum f\left | X-Median \right |}{\sum f}$

The mean deviation about the mode is

$\large M.D (about\;mode)=\frac{\sum f\left | X-Mode\right |}{\sum f}$

For a population data the mean deviation about the population mean $\mu$ is

$\large M.D=\frac{\sum f\left | X-\mu \right |}{\sum f}$

### Solved Example:

Question 1: Anubhav scored 85, 91, 88, 78, 85 for a series of exams. Calculate the mean deviation for his test scores?

Ans:  Given test score; 85, 91, 88, 78, 85

Mean, $\bar{x}$ = (85+91+88+78+85)/5

= 85.4

Subtracting mean from each score;

 x $\mathbf{x_i – \bar{x}}$ $\mathbf{|x_i – \bar{x}|}$ 85 -0.4 0.4 91 5.6 5.6 88 2.6 2.6 78 -7.4 7.4 85 -0.4 0.4

Mean deviation = 16.4/5 = 3.28

Thus we can say that, on average the student’s test scores vary by a deviation of 3.28 points from the mean.
 More topics in Mean Deviation Formula Average Deviation Formula Mean Absolute Deviation Formula

#### Practise This Question

Fractional distillation is the separation of a mixture into its component or fractions. This process is based on difference in boiling point of the components in the mixture. This is a special type of distillation.

Air is a homogeneous mixture of 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases such as helium, krypton, nitrogen dioxide etc.

Consider three gases oxygen, nitrogen and argon whose boiling points are: -183, -196, -186 degree celsius. They are to be separated from air using fractional distillation.

Air is compressed by increasing pressure and is then cooled by decreasing the temperature to form liquid air. This liquid air is allowed to warm-up slowly in a fractional distillation column, where gases get separated at different heights depending upon their boiling points. As the height of tower increases the temperature increases.

Among the three gases, which gas is collected at last?