Question

Consider the following frequency distribution:

Class	$0-5$	$6-11$	$12-17$	$18-23$	$24-29$
Frequency	$13$	$10$	$15$	$8$	$11$

The upper limit of the median class is ____________ .

• A. $17$
• B. $17.5$
• C. $18$
• D. $18.5$

Answer 1

The correct option is B

$17.5$

Explanation for the correct option:

Step 1: Find the total number of observations

For finding the median class we need to calculate the cumulative frequency and convert the data into the continuous format by adding $0.5$ to the upper limit and subtracting the same from the lower limit.

Cumulative frequency is the sum of the preceding all the frequencies to that class interval whose cumulative frequency is to be found.

Let's write the given data in continuous distribution format and find the cumulative frequency:

Class	Frequency	Cumulative Frequency
$0.5-5.5$	$13$	$13$
$5.5-11.5$	$10$	$23$
$11.5-17.5$	$15$	$38$
$17.5-23.5$	$8$	$46$
$23.5-29.5$	$11$	$57$

So, the number of observations, $N=57$

Step 2: Find the upper limit of the median class

$N=57$, that is an odd number.

The median for the odd number of observations is given by: $=\frac{\mathrm{N}}{2}$

$=\frac{57}{2}$

$=28.5$

The cumulative frequency just after $28.5$ is $38$.
That means, $28.5$ lies in between the interval $11.5-17.5$.

Therefore, the upper limit of median class is $17.5$.

Hence ,option (B) is correct.