Question

Find the median for the following data given below:

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

• A. $5.3$
• B. $5.4$
• C. $5.1$
• D. $5.6$

Answer 1

The correct option is B $5.4$

Class Interval	Frequency(f)	Cumulative Frequency (cf)
0-2	2	2
2-4	3	5
4-6	5	10
6-8	7	17
	$n=\Sigma f=17$

Here, $\frac{n}{2}=\frac{17}{2}=8.5$

Hence, the median class is $4-6$

We know that,

Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
Where, $l\to$ lower limit of the median class $=4$
$n=\Sigma f\to$ total number of frequency $=17$
$cf\to$ cumulative frequency of the class preceding the median class $=5$
$f\to$ frequency of the median class$=5$
$h\to$ class width $=2$
Therefore, Median $=4+\left(\frac{\frac{17}{2}-5}{5}\right)\times 2$
$\Rightarrow 4+\left(\frac{17-10}{2\times 5}\right)\times 2$
$\Rightarrow 4+1.4$
$\Rightarrow 5.4$
Hence, the median for the given data is $5.4$