Answer the following questions in detail−

Calculate the mode from the following fequency distribution

Sales in crores 0-4 4-8 8-12 12-16 16-20 20-24

No. of firms 4 6 12 7 6 3

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Solution

C.I.

f

0–4

4

4–8

f₀ - 6

8–12

f₁ - 12

→ Modal Class

12–16

f₂- 7

16–20

6

20–24

3

In the given series, (8–12) is the modal class, as it has the highest frequency of 12.
In such case, the mode is calculated as follows:

$Mode = L_{1} + \frac{(L_{2} - L_{1}) (f_{1} - f_{0})}{2 f_{1} - f_{0} - f_{2}} = 8 + \frac{(12 - 8) (12 - 6)}{2 \times 12 - 6 - 7} = 8 + \frac{24}{11} = 5.82$

Suggest Corrections

Marks	0−4	4−8	8−12	12−16	16−20	20−24
No. of Students	7	9	16	8	6	4

Class Interval	4−8	8−12	12−16	16−20	20−24	24−28	28−32	32−36	36−40
Frequency	10	12	16	14	10	8	17	5	4

Daily wages (in ₹)	2−4	4−6	6−8	8−10	10−12	12−14	14−16	16−18
No. of Workers	11	14	20	32	25	7	5	2