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## SS2: ECONOMICS - 1ST TERM

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Lesson 1, Topic 5
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# The Mean Deviation

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#### Topic Content:

• Definition of Mean Deviation
• Procedure for Calculating Mean Deviation

### What is Mean Deviation?

Mean deviation is the average deviation of the mean, it shows how far the average of the observations is from the mean. Mean deviation is given as the sum of the absolute deviations.

M.D = $$\frac{\sum \left | X \: – \: \bar{X} \right |}{n}$$

or

$$\frac{\sum d}{n}$$ $$\frac{1}{n}\scriptsize \sum |x| \: – \: |\bar{x}|$$ (Ungrouped data)

M.D = $$\frac{\sum f \left | x \: – \: \frac{n}{x} \right |}{n}$$

or

$$\frac{\sum f d}{\sum f}$$ (Grouped data)

n = no of scores

|     | (the vertical bars) mean Absolute Value, basically to ignore any minus sign.

ā = sum of observation

x = score

$$\scriptsize \bar{x}$$ = mean

d = deviation

### Procedure for Calculating Mean Deviation:

Step I:            Calculate the mean
Step II:           Subtract the mean from each score
Step III:          Add up the total deviation and divide by the number of scores

### Example 1.4.1:

Find the mean deviation of the following set of scores: 41, 30, 36, 37, 39, 45, 34, 45, 48, 45 calculate the mean.

Solution:

Use the formula:

M.D = $$\frac{\sum | X \: – \: \bar{X}|} {n}$$ or $$\frac{\sum d}{n}$$

Step I: Calculate the mean

$$\scriptsize \bar{X} = \normalsize \frac{30 \: +34\: +\:36\: +\:37\: +\:41\: +\:39\: \\ +\:45\: +\:45\: +\:45\: +\:48}{10} \\ = \frac{400}{10} \\ = \scriptsize 40$$

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