Arithmetic mean of the following series is 41:

Marks 20 30 40 ? 60 70

No. of Students 8 12 20 10 6 4

Find the missing item

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Solution

Marks
(X) No. of Students (f) fX

20
30
40
x
60
70 8
12
20
10
6
4 160
360
800
10x
360
280

$Σ f =$ 60 $Σ f X$ =1960 + 10x

Given:

Mean, $X$ = 41

$X = \frac{Σ X}{Σ f} 41 = \frac{1960 + 10 x}{60} o r, 41 \times 60 = 1960 + 10 x o r, 2460 - 1960 = 10 x o r, 500 = 10 x o r, x = \frac{500}{10} \Rightarrow x = 50 m a r k s$

Hence, the missing item is 50 marks

Suggest Corrections

Marks	10−20	20−30	30−40	40−50	50−60	60−70
No. of Students	8	11	9	25	12	16

Mark	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No. of students	8	10	15	25	20	18	9	5

Marks	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90
No. of students	7	13	20	25	10	8	6	1

Marks	0−10	10−20	20−30	30−40	40−50
Number of Students	8	30	40	12	10

Marks	10−20	20−30	30−40	40−50	50−60
No. of students	12	18	14	63	19