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

Maharashtra BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive5 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 $x_i$
$d_i = x_i − 25$
$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_\text{i}-25}{10}$
$f_i \times u$_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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