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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 the assumed-mean method:
Class
100-120
120-140
140-160
160-180
180-200
Frequency
10
20
30
15
5
✓

Answer

We have, Let A = 25 be the assumed mean
Marks
Frequency $f_i$
Mid-value $x_1$
Deviation $d_i = x_i- 150$
$f_1 \times d_1$
100-120
10
110
-40
-400
120-140
20
130
-20
-400
140-160
 30
150 = A
0
0
160-180
15
170
20
300
180-200
5
190
40
200
 
$\sum\text{f}_\text{i}=80$
 
 
$\sum\text{f}_\text{i}\times\text{d}_\text{i}=-300$
$\bar{\text{x}}=\text{A}+\frac{\sum(\text{f}_\text{i}\times\text{x}_\text{i})}{\sum\text{f}_\text{i}}$
$=\Big(150+\frac{-300}{80}\Big)=(150-3.75)=146.25$Hence mean = 146.25

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