Question
Find out the mean deviation from arithmetic mean from the given data.
Class lnterval: 0-10 10-20 20-30 30-40 40-50
Frecquency: 2 4 6 4 2

Answer

Calculation of Mean Deviation from Arithmetic Mean
Class lnterval Frequency (f) Mid value (m) fm $|\text{D}|=|\text{m}-\bar{\text{X}}|\bar{\text{X}}=25$ $\text{f|D}|$
0-10 2 5 10 20 40
10-20 4 15 60 10 40
20-30 6 25 150 0 0
30-40 4 35 140 10 40
40-50 2 45 90 20 40
  $\sum\text{f}=18$   $\sum\text{fm}=450$   $\sum\text{f|D|}=160$
$\bar{\text{X}}=\frac{\sum\text{fm}}{\sum\text{f}}=\frac{450}{18}=25$
$\therefore\bar{\text{X}}=25$
Mean Deviation from Mean $(\text{MD}_{\bar{\text{X}}})$
$=\frac{\sum\text{f|D|}}{\sum\text{f}}$
$=\frac{160}{18}=8.89$

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