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 median class is :

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

Answer 1

The correct option is B

$17.5$

Solution:

Draw the frequency distribution table to find cumulative frequency:

Converting the data into continuous frequency distribution by adding $0.5$to upper limit and subtracting $0.5$ to lower limit, we get,

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

Here, total number of observations $n=57$, which is an odd number

Calculate median:

Median $={\left(\frac{57+1}{2}\right)}^{\mathrm{th}}\mathrm{term}$ $\left[\because Median={\left(\frac{n+1}{2}\right)}^{th}term,whennisodd\right]$

$={29}^{th}\mathrm{term}$

Here, ${29}^{\mathrm{th}}$term lies in class $11.5-17.5$

$\therefore$Upper limit of median class is $\mathbf{17}\mathbf{.}\mathbf{5}$.

Final Answer:

Option (B) is correct answer.