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What is the mean deviation of the data 2, 9, 9, 3, 6, 9, 4 ?
1. 2.23
2. 2.57
3. 3.23
4. 3.57

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Correct Answer - Option 2 : 2.57

Concept:

To find the mean deviation, use the following steps

Step 1: Find the mean value for the given data values

Step 2: Now, subtract mean value form each of the data value given (Note: Ignore the minus symbol)

Step 3: Now, find the mean of those values obtained in step 2.

Mean deviation \(\rm = \dfrac {1}{n} \sum |x - \bar x|\)

Calculations:

Given data is 2, 9, 9, 3, 6, 9, 4 

⇒ n = 7

Mean \(\rm \bar x = \dfrac {2+9+9+3+6+9+4}{7}\)

⇒  \(\rm \bar x = 6\)

Mean deviation \(\rm = \dfrac {1}{n} \sum |x - \bar x|\)

⇒ Mean deviation \(\rm = \dfrac {1}{7} {(|2-6|+|9-6|+|9-6|+|3-6|+ \|6-6|+|9-6+|4-6|)}\)

⇒ Mean deviation =  2.57

Hence, the mean deviation of the data 2, 9, 9, 3, 6, 9, 4 is 2.57

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