find the value of p if the mean of given frequency distribution table is 15
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ARITHMETIC MEAN OR MEAN OR AVERAGE :
The arithmetic mean of a set of observations is obtained by dividing the sum of the values of all observations by the total number of observations .
Mean = Sum of all the observations / Total number of observations .
MEAN = Σfixi / Σfi
[‘Σ’ Sigma means ‘summation’ ]
FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT
From the table : Σfixi = 445 + 10p , Σfi = 27 + p
MEAN = Σfixi / Σfi
Given : Mean = 15
15 = (445 + 10p) / (27 + p)
15 × (27 + p) = 445 + 10p
405 + 15p = 445 + 10p
15p - 10p = 445 - 405
5p = 40
p = 40/5 = 8
p = 8
Hence, the value of ‘p’ is 8.
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