) The arithmetic mean of the following frequency distribution is 67.45. Height (inch) 61 64 67 70 73 Frequency 15 54 F3 81 24 Required: Find the value of F3. (
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Explanation:
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The Arithmetic Mean of the following frequency distribution is 47 Determined the value of p
C.I. 0−20 20−40 40−60 60−80 80−100
Frequency 8 15 20 p 3
Medium
Solution
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Correct option is
A
12
Calculation of Arithmetic Mean
C.I. Frequency
(f
i
)
Class Mark
(x
i
)
u
i
=f
i
x
i
0 - 20 8 10 80
20 - 40 15 30 450
40 - 60 20 50 1000
60 - 80 p 70 70p
80 - 100 30 90 450
Total 48 + p 1980 + 70 p
x
ˉ
=
∑f
i
∑f
i
x
i
=
48+p
1980+70p
∴
48+p
1980+70p
=47
⇒1980+70p=47(48+p)
⇒1980+70p=(47)(48)+47p
⇒1980+70p=2256+47p
⇒70p−47p=2256−1980
⇒23p=276
⇒p=
23
276
=12
Hence p=12