Find the median of the following data:

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Frequency 5 3 4 3 3 4 7 9 7 8

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Solution

The cumulative frequency table for the given data is shown below.

$\frac{N}{2} = \frac{53}{2} = 26.5$
Cumulative frequency just greater than 26.5 is 29.
The corresponding class interval is 60 - 70.
Thus, median class is 60 - 70.
Cumulative frequency just before this class = 22
So, l = 60, f = 7 , $\frac{N}{2} = 26.5$ , h = 10 and cf = 22
$Median, M_{e} = l + \{h \times \frac{(\frac{N}{2} - c f)}{f}\}$
$= 60 + \{10 \times (\frac{26.5 - 22}{7})\} = 60 + \frac{10 \times 4.5}{7} = 60 + 6.43 = 66.43$
Hence, median = 66.43

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Similar questions

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	5	3	4	3	3	4	7	9	7	8

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90	90−100
Number of students	5	3	4	3	3	4	7	9	7	8

Items	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Frequency	5	10	16	18	12	10	8

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	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	6	8	10	15	5	4	2

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