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Measures of Central Tendency — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Central Tendency6 Marks
Question
If the arithmetic mean of the data given below is 28, find out the missing frequency:
X
0-10
10-20
20-30
30-40
40-50
50-60
f
12
18
27
-
17
6
✓

Answer

Let the missing frequency be Y.
Class
f
M.V. (m)
fm
0-10
12
5
60
10-20
18
15
270
20-30
27
25
675
30-40
Y
35
35Y
40-50
17
45
765
50-60
6
55
330
 
$\Sigma\text{f}=80+\text{Y}$
 
$\Sigma\text{fm}=2100+35\text{Y}$
$\overline{\text{X}}=\frac{\Sigma\text{fm}}{\Sigma\text{f}}\Rightarrow28=\frac{2100+35\text{Y}}{80+\text{Y}}$
$\Rightarrow\ 28(80+\text{Y})=2100+35\text{Y}$
$\Rightarrow\ 2240+28\text{Y}=2100+35\text{Y}$
$\Rightarrow\ 140=7\text{Y}\Rightarrow\ \text{Y}=\frac{140}{7}=20$
Hence, the missing frequency is 20.$\text{Note}\Rightarrow\ \Sigma\text{f}=\text{N}$

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