The following distribution shows the daily pocket allowance of children of a locality.

To find the class mark (xᵢ) for each interval, the folowing relation is used.
xᵢ = (Upper limit + Lower limit)/2
Given that the mean nocket allawance is ₹18 Taking 18 as.assured mean (a), dᵢ and fᵢdᵢ are calculated as follows:

From the table, we obtain
∑fᵢ = 44 + f, ∑fᵢdᵢ = 2f – 40 and a = 18
mean(X̄) = a + (∑fᵢdᵢ)/∑fᵢ ⇒ 18 = 18 + ((2F – 40)/(44 + F)) ⇒ 0 = (2F – 40)/(44 + f) ⇒ 2f – 40 = 0 ⇒ f = 20
Hence, the value of missing frequency f is 20.

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