Q. 83.7( 47 Votes )
The mean of the following frequency distribution is 50 but the frequencies f1 and f2 in classes 20 - 40 and 60 - 80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.
First, we calculate the class mark of given data
Given that, sum of all frequencies = 120
assumed mean, a = 50 and
class width, h = 20
By step deviation method,
⇒ 4 + f2 - f1 = 0
⇒ -f2 + f1 = 4 - - - - (ii)
On adding Eqs. (i) and (ii), we get
2f1 = 56
⇒ f1 = 28
Put the value of in Eq. (i), we get
f2 = 52 - 28
⇒ f2 = 24
Hence, f1 = 28 and f2 = 24
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