Find median for the following data.
$X$
$0 - 5$
$5 - 10$
$10 - 15$
$15 - 20$
$20 - 25$
frequency
$2$
$4$
$6$
$8$
$10$

4

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5

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7

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6

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Solution

The correct option is C $7$
Form a cumulative frequency table:
x
frequency (f)
cumulative frequency
(cf)
0-5
2
2
5-10
4
2 + 4 = 6
10-15
6
6 + 6 = 12
15-20
8
12 + 8 = 20
20-25
10
20 + 10 = 30

n = $\sum F = 30$
$\frac{n}{2} = \frac{30}{2} = 15$

Median = $l + (\frac{\frac{n}{2} - c f}{f} \times h)$
i = lower limit of the median class = 15
n = $\sum F$ = total number of frequency = 15
So, the median class is 15-20
Cf = cumulative frequency of the class preceding the median class = 20
f = frequency of the median class = 8
h = class width = 5
Therefore, Median = $l + (\frac{\frac{n}{2} - c f}{f} \times h)$
Median = $15 + (\frac{\frac{15}{2} - 20}{8} \times 5)$
= $15 + (\frac{- 12.5}{8} \times 5)$
= 15 - 7.8125
= 7.18 $\approx$ 7

Suggest Corrections

Variable( $x$ )	$10$	$15$	$20$	$25$	$30$	$35$	$40$	45
Frequency( $f$ )	$7$	$3$	$8$	$5$	$6$	$8$	$4$	9

$X$	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$
frequency	$2$	$4$	$6$	$8$	$10$

Class-interval	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
Frequency	$5$	$3$	$9$	$10$	$8$	$5$

Class:	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
Frequency	$4$	$5$	$7$	$12$	$7$	$5$