Q) Find the mean and the mode of the following frequency distribution:

(Q 33 – 30/3/3 – CBSE 2026 Question Paper)

Ans:

(i) Mean value: Let’s rearrange the data:

Now, from this improved table, we have:

∑fx = 6240 and ∑f = 120

∴ Mean =

∴ Mean = = 52

Therefore, the mean value of the given grouped data is 52.

(ii) Mode value:.

Since the frequency is highest in “30-45”

∴ “30-45” is the modal class

Since the mode value is calculated by = L +

Here, L = 10, f₀ = 15, f₁ = 35, f₂ = 20 and h = 45-30 = 15

∴ Mode = L +

= 30 +

= 30 +  = 30 +

= 30 +  = 30 +

= 30 + 8.57 = 38.57

Therefore, the mode value of the given grouped data is 38.57.

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