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What is the coefficient of mean deviation of 21, 34, 23, 39, 26, 37, 40, 20, 33, 27 (taken from mean)?

A.
0.11
B.
0.22
C.
0.33
D.
0.44

Solution:

Concept:Mean deviation from mean = \(\displaystyle \frac{??xi? ? x? ??}{N}\) Coefficient of mean deviation = \(\displaystyle \frac{Mean\ Deviation}{? x}\)where N is the number of observationx? is the mean of the datax is the value of the observation.Calculation:\(\displaystyle Mean=? x=\frac{Sum\ of \ observation\ }{Number\ of \ observation}\)\(\displaystyle Mean=? x=\frac{21+34+23+39+26+37+40+20+33+27}{10}\)? x? = \(\displaystyle \frac{300}{10}=30\) Sum of deviation from mean is given by ??xi? ? x??,? ??xi? ? x?? = ?21 ? 30? + ?34 ? 30? + ?23 ? 30? + ?39 ? 30? + ?26 ? 30? + ?37 ? 30? + ?40 ? 30? + ?20 ? 30? + ?33 ? 30? + ?27 ? 30?? ??xi? ? x?? = 9 + 4 + 7 + 9 + 4 + 3 + 10 + 10 + 7 + 3? ??xi? ? x?? = 66Mean deviation from mean = \(\displaystyle \frac{??xi? ? x? ??}{10}\) = \(\displaystyle \frac{66}{10}\) ?= 6.6Coefficient of mean deviation = \(\displaystyle \frac{6.6}{30}\) = 0.22? Coefficient of mean deviation = 0.22

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