Q) If the median of the following frequency distribution is 32.5 and sum of all frequencies is 40, then find the values of f1 and f2:

(Q 35 B – 30/5/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Given that the total of frequencies = 40

∴ 32 + f₁ + f₂ = 40

∴ f₁ + f₂ = 40 – 32

∴ f₁ + f₂ = 8 ……… (i)

Step 2: To find the median, we need to identify middle value of the data. Let’s rearrange the data:

• First, we will need cumulative frequency to find the median. Its shown in last column.
• Next, we will need Total of frequencies. It shown in the last row of middle column (= 32 + f₁ + f₂)
• Next, we need to identify Median Class. Since, the Median class is the class where the cumulative frequency crosses 50% of the total of frequencies. Here total to frequencies is 40 (given) and its 50% is 20.
• In the above modified data table, cumulative frequency of (12 + f₁) at class “20-30” is not crossing 20, but cumulative frequency of (24 + f₁) at class “30-40” is crossing 20. Hence, our Median class = 30-40
  (Another logic: Given Median of 32.5 will lie in “30-40” class only)

Now, we calculate the median by using the formula:
Median = L + h

Here:

L = Lower boundary of the median class = 30
n = Total number of Classes = 40
C_f = Cumulative frequency of the class before the median class = 12 + f₁
f = Frequency of the median class = 12
h = Class width = 40 – 30 = 10

∴ 32.5 = 30 + (10)

∴ 2.5 = (10)

∴ 2.5 x 12 = (8 – f₁) 10

∴ 30 = (8 – f₁) 10

∴ 3 = 8 – f₁

∴ f₁ = 8 – 3

∴ f₁ = 5

Step 3: By substituting the value of f₁ in equation (i), we get:

f₁ + f₂ = 8

∴ f₂ = 8 – f₁ = 8 -5

∴ f₂ = 5

Therefore, the values of frequencies, f₁ and f₂ are 5 and 3 respectively

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