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Find the mean deviation from mean of the following distribution.
written 4.7 years ago by gravatar for teamques10 teamques10 ★ 64k •   modified 4.7 years ago
C.I 0-10 10-20 20-30 30-40 40-50
$F_{i}$ 5 8 15 16 6
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written 4.7 years ago by gravatar for teamques10 teamques10 ★ 64k

Solution:

C.I $f_{i}$ $x_{i}$ $f_{I}x_{i}$ $d_{I}=|x_{I}-\bar{x}|$ $f_{I}d_{i}$
0-10 5 5 25 22 110
10-20 8 15 120 12 96
20-30 15 25 375 2 30
30-40 16 35 560 8 128
40-50 6 45 270 18 108
$\sum f_{I}=50$ $\sum f_{i} x_{I}=1350$ $\sum f_{i} d_{i}=472$

$\operatorname{Mean} \overline{x}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$\therefore \overline{x}=\frac{1350}{50}$

$\therefore \overline{x}=27$

$M \cdot D=\frac{\sum f_{i} d_{i}}{f_{i}}$

$\therefore M \cdot D=\frac{472}{50}$

$\therefore M \cdot D .=9.44$
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