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Measures Of Central Tendency — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMeasures Of Central Tendency4 Marks
Question
Find the mean of the following frequency distribution by the step deviation method : 
Class  $0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$ $120-140$
Frequency  $12$ $24$ $52$ $88$ $66$ $42$ $16$
✓

Answer

Class Interval $x_i$ $f_i$ $ A =70 , u =\frac{ x - A }{ h _i}$ $f_i u$
$0-20 $ $10$ $12$ $-3$ $-36$
$20-40$ $30$ $24$ $-2$ $-48$
$40-60$ $50$ $52$ $-1$ $-52$
$60-80$ $A = 70$ $88$ $0$ $0$
$80-100$ $90$ $66$ $1$ $66$
$100-120$ $110$ $42$ $2$ $84$
$120-140$ $130$ $16$ $3$ $48$
Total   $300$   $62$
$ A =70 $ and $h _{ i }=20$
$\bar{x}= A + h \times \frac{\Sigma f_i u }{\Sigma f_i}$
$\bar{x}=70+20 \times \frac{62}{300}$
$\bar{x}=70+4.13$
$\bar{x}=74.13$
$\therefore \text { Mean }=74.13$

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