Find the mean and the mode of the following frequency

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 = $\frac{\sig fx}{\sig f}$

∴ Mean = $\frac{6240}{120}$ = 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 + $\left[\frac{f_0-f_1}{2f_0 - f_1-f-2}\right] h$

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

∴ Mode = L + $\left[\frac{f_0-f_1}{2f_0 - f_1-f-2}\right] h$

= 30 + $\left[\frac{35-(15)}{2 (35) - (15) - (20)}\right] (15)$

= 30 + $(\frac{20}{35})(15)$ = 30 + $(\frac{4}{7})(15)$

= 30 + $(\frac{(4)(15)}{7})$ = 30 + $(\frac{60}{7})$

= 30 + 8.57 = 38.57

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

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