The scores obtained by 6 students in a test are 18, 21, 25, 16, 12, 24. Calculate mean deviation about mean using the assumed mean method.

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Solution

The correct option is C 4
$M e a n, ¯ X = \frac{18 + 21 + 25 + 16 + 12 + 24}{6} = \frac{116}{6} = 19.33$

Let the assumed mean (A) be 20.

Deviations from the assumed mean are tabulated below

$\begin{matrix} X & D = | X - A | 18 & 2 21 & 1 25 & 5 16 & 4 12 & 8 24 & 4 \sum D = 24 \end{matrix}$

$M . D (¯ X) = \frac{\sum D + (¯ X - A) (\sum f_{B} - f_{A})}{n} = \frac{24 + (20 - 19.33) (3 - 3)}{6} = \frac{24}{6} = 4$

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The scores obtained by 6 students in a test are 18, 21, 25, 16, 12, 24. Calculate mean deviation about mean using the assumed mean method.

The correct option is C 4Mean,¯X=18+21+25+16+12+246=1166=19.33 Let the assumed mean (A) be 20. Deviations from the assumed mean are tabulated below XD=|X−A|182211255164128244∑D=24 M.D(¯X)=∑D+(¯X−A)(∑fB−fA)n=24+(20−19.33)(3−3)6=246=4