Calculate the arithmetic average from the following data:

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

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Solution

Class Interval
(Wages) Mid Values
(m) Workers
(f) fm

2 − 4
4 − 6
6 − 8
8 − 10
10 − 12
12 − 14
14 − 16
16 − 18 3
5
7
9
11
13
15
17 11
14
20
32
25
7
5
2 33
70
140
288
275
91
75
34

$Σ f$ =116 $Σ f m$ =1006

Calculating the average wage using direct method:

$X = \frac{Σ f m}{Σ f} or, X = \frac{1006}{116} \Rightarrow X = Rs 8.67$

Hence, average daily wage is Rs 8.67

Suggest Corrections

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

Valuable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	7	12	18	25	16	14	8

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

Daily Wage (₹)	6	7	8	9	10	11	12	15
Number of Workers	10	15	12	18	25	20	10	4

Size	20	19	18	17	16	15	14	13	12	11
Frequency	1	2	4	8	11	10	7	4	2	1