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Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive4 Marks
Question
Find the mean of the following frequency distribution using step-deviation method.
Class
$0-10$
$10-20$
$20-30$
$30-40$
$40-50$
Frequency
$7$
$10$
$15$
$8$
$10$
✓

Answer

Class interval
Frequency $f_i$
Mid-value $x_i$
$d_i= x_i− 25$
$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_\text{i}-25}{10}$
$f_i× u_i$
$0-10$
$7$
$5$
$−20$
$−2$
$−14$
$10-20$
$10$
$15$
$−10$
$−1$
$−10$
$20-30$
$15$
$25$
$0$
$0$
$0$
$30-40$
$8$
$35$
$10$
$1$
$8$
$40-50$
$10$
$45$
$20$
$2$
$20$
 
$\sum\text{f}_\text{i}=50$
 
 
 
$\sum\text{f}_\text{i}\text{u}_\text{i}=4$
Thus, $\text{A}=25,\ \text{h}=10,\ \sum\text{f}_\text{i}=50$ and $\sum\text{f}_\text{i}\text{u}_\text{i}=4$
Mean $=\text{A}+\Big\{\text{h}\times\frac{\sum\text{f}_\text{i}\text{u}_\text{i}}{\sum\text{f}_\text{i}}\Big\}$
$25+\Big\{10\times\frac{4}{50}\Big\}$
$=25.08$
$=25.8$

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