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Mean, Median, Mode of Grouped Data — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data5 Marks
Question
Find the mean of the following data, using step-deviation method.
Class
5-15
15-25
25-35
35-45
45-55
55-65
65-75
Frequency
6
10
16
15
24
8
7
✓

Answer

Class interval
Frequency $f_i$
Mid-value $x_i$
$d_i = x_i − 25$
$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_\text{i}-40}{10}$
$f_i \times u_i$
5-15
 6 10
-30
 -3
-18
15-25
10
 20
-20
 -2
-20
25-35
16
 30
-10
 -1 -16
35-45
 15 40
0
 0 0
45-55
24
 50
10
 1 24
55-65 8 60 20 2 16
65-75 7 70 30 3 21
 
$\sum\text{f}_\text{i}=86$
 
 
 
$\sum\text{f}_\text{i}\text{u}_\text{i}=7$
Thus, $\text{A}=40,\ \text{h}=10,\ \sum\text{f}_\text{i}=86$ and $\sum\text{f}_\text{i}\text{u}_\text{i}=7$
Mean $=\text{A}+\Big\{\text{h}\times\frac{\sum\text{f}_\text{i}\text{u}_\text{i}}{\sum\text{f}_\text{i}}\Big\}$
$40+\Big\{10\times\frac{7}{86}\Big\}$
$=40+0.81$
$=40.81$

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