Consider the following frequency distribution.

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	4	5	7	10	12	8	4

Find the median of the distribution?

The median is the middle value that divides the data into two equal halves.

Creating a cumulative frequency table:

Class	Frequency (f)	Cumulative Frequency (cf)
0-10	4	4
10-20	5	9
20-30	7	16
30-40	10	26
40-50	12	38
50-60	8	46
60-70	4	50

Total frequency $N = 50$

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Finding the middle position:

$\dfrac{N}{2} = \dfrac{50}{2} = 25$

The median is the 25th value when all data is arranged in order.

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The median class is the first class where cumulative frequency is greater than or equal to 25.

Looking at the cumulative frequency column:

• At class 20-30: cf = 16 (less than 25)
• At class 30-40: cf = 26 (greater than 25)

Median Class = 30-40

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Using the median formula:

Median $= L + \left[\dfrac{N/2 - cf}{f}\right] \times h$

Where:

• $L = 30$ (lower boundary of median class)
• $N/2 = 25$
• $cf = 16$ (cumulative frequency before median class)
• $f = 10$ (frequency of median class)
• $h = 10$ (class width)

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Median $= 30 + \left[\dfrac{25 - 16}{10}\right] \times 10$

Median $= 30 + \left[\dfrac{9}{10}\right] \times 10$

Median $= 30 + 0.9 \times 10$

Median $= 30 + 9$

Median $= 39$

Therefore, the median of the distribution is 39.