Find the mean of the following data by shortcut method.

Marks 20 22 25 30 35 39 45 50 Total

Frequency 4 6 8 10 8 7 5 2 50

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Solution

We have,

Let the marks be represented as x_i and frequency be represented as f_i.

Let a = 30

$So, x = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}} = 30 + \frac{90}{50} = 30 + 1.8 = 31.8$

Hence, the mean of the given data is 31.8.

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Class Interval	20−25	25−30	30−35	35−40	40−45	45−50	50−55
Frequency	10	12	8	20	11	4	5

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

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	7	5	6	12	8	2

Class	0−10	10−20	20−30	30−40	40−50
Frequency	7	10	15	8	10

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

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