Calculate mean from following data:

Marks 5−15 15−25 25−35 35−45 45−55 55−65

No. of Students 8 12 6 14 7 3

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Solution

Class Interval
(Marks) Mid-Values
(m) Students
(f) fm

5 − 15
15 − 25
25 − 35
35 − 45
45 − 55
55 − 65 10
20
30
40
50
60 8
12
6
14
7
3 80
240
180
560
350
180

Σf= 50 Σfm= 1590

Calculating mean marks by using direct method:

$X = \frac{Σ f m}{Σ f} or, X = \frac{1590}{50} \Rightarrow X = 31.8 marks$

Hence, mean of the above series is 31.8 marks

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Class	5−15	15−25	25−35	35−45	45−55	55−65	65−75
Frequency	6	10	16	15	24	8	7

Income	15−24	25−34	35−44	45−54	55−64	65−74
No. of Workers	8	10	15	25	40	20

Wage Rate (₹)	5−15	15−25	25−35	35−45	45−55	55−65
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Number of Students	7	13	10	15	30	33	28	14

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