Calculate the mean from the following frequency distribution:

X 10−19 20−29 30−39 40−49 50−59 60−69 70−79 80−89

No. Persons 32 42 40 56 20 6 2 2

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Solution

Class interval
(X)
Mid-Values
(m) No. of persons
(f) fm

10 − 19
20 − 29
30 − 39
40 − 49
50 − 59
60 − 69
70 − 79
80 − 89 14.5
24.5
34.5
44.5
54.5
64.5
74.5
84.5 32
42
40
56
20
6
2
2 464
1029
1380
2492
1090
387
149
169

$Σ f$ =200 $Σ f m$ =7160

Calculating the mean from the above inclusive series by using direct method:

$X = \frac{Σ f m}{Σ f} o r, X = \frac{7160}{200} \Rightarrow X = 35.8$

Hence, the mean of the above series is 35.8

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Age (Years)	80−89	70−79	60−69	50−59	40−49	30−39	20−29	10−19
Frequency	2	2	6	20	56	40	42	32

Marks	10−19	20−29	30−39	40−49	50−59	60−69	70−79	80−89	90−99
Number of Students	29	87	181	247	263	133	40	9	2

Calculate the mean for the following frequency distribution:

Marks	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	3	7	10	6	8	2	4

Class-intervals	10−29	30−39	40−49	50−59	59−60	60−69
Frequencies	12	19	20	21	15	13

Class Interval	60−69	50−59	40−49	30−39	20−29	10−19
Frequency	13	15	21	20	19	12

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