Question
Calculate mean deviation from mean $(\text{M.D.}_{\bar{\text{X}}})$ from the given data:
Marks obtained: 140-150 150-160 160-170 170-180 180-190 190-200
No. of girls: 4 6 10 18 9 3

Answer

X M.V. (m) f dx dx'(dx/i) fdx' |dx| f|dx|
140-150 145 4 -20 -2 -8 26.6 104.8
150-160 155 6 -10 -1 -6 16.2 97.2
160-170 165 10 0 0 0 6.2 62.0
170-180 175 18 10 1 18 3.8 68.4
180-190 185 9 20 2 18 13.8 124.2
190-200 195 3 30 3 9 23.8 71.4
    $\Sigma\text{f}=50$     $\Sigma\text{fd}'=31$   $\Sigma\text{f|dx|}=528.0$
Mean $=\text{A}+\frac{\Sigma\text{fd}'}{\Sigma\text{f}}\times\text{i}$
$=165+\frac{31}{50}\times10=171.2$
$\text{M.D.}_{\bar{\text{X}}}=\frac{\Sigma\text{f|dx|}}{\Sigma\text{f}}=\frac{528}{50}=10.56$

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