What is the median for the following data?
$x$
$2 - 4$
$4 - 6$
$6 - 8$
$8 - 10$
$10 - 12$
frequency
$1$
$3$
$2$
$4$
$10$

6

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6.5

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7

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7.5

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Solution

The correct option is C $7$

X

Frequency

Cumulative frequency(position)

$2 - 4$

$1$

$1$

$4 - 6$

$3$

$4$

$6 - 8$

$2$

$6$

$8 - 10$

$4$

$10$

$10 - 12$

$10$

$20$

Sum of frequency $= 20$
Sum of frequency is even. So, Median is
Average of $(\frac{n}{2}) & (\frac{n}{2} + 1) p o s i t i o n \frac{n}{2} = \frac{20}{2} = 10 \frac{20}{2} + 1 = 11 10 t h p o s i t i o n = 4 11 t h p o s i t i o n = 10 A v e r a g e = \frac{4 + 10}{2} = 7 A n s$

Suggest Corrections

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

$x$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$
frequency	$1$	$3$	$2$	$4$	$10$

X	Frequency	Cumulative frequency(position)
$2 - 4$	$1$	$1$
$4 - 6$	$3$	$4$
$6 - 8$	$2$	$6$
$8 - 10$	$4$	$10$
$10 - 12$	$10$	$20$

Class interval	$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$
Frequencies	$2$	$3$	$5$	$7$