Q) The following distribution shows the daily pocket allowance of children of a locality. The mean daily pocket allowance is < 36.10. Find the missing frequency, f.
Ans: Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency:
We know that the mean value of a grouped data is given by:
Mean Value of grouped data = 
from above table, we have: Σfx = 1550 + 42.5 f and Σf = 44 + f
∴ mean value = 
Given that the mean value of grouped data is 36.10
∴ 36.10 =
∴ 36.10 (44 + f) = (1550 + 42.5 f)
∴ 36.10 x 44 + 36.10 f = 1550 + 42.5 f
∴ 36.10 x 44 – 1550 = 42.5 f – 36.10 f
∴ 1588.4 – 1550 = 42.5 f – 36.10 f
∴ 38.4 = 6.4 f
∴ f = 
∴ f = 6
Therefore the value of the missing frequency, f is 6.
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