Question

1. Find the modal class.
2. Find the median

Answer 1

$\purple{ \huge✏ \underline{ \boxed{ \bf \red{ANSWER : }}}}$

$\green{ \mathbb { \underline{\underline{MODAL \: CLASS : }}}}$

Modal class is a class with the maximum frequency .

Here, Class 0 - 2 has highest frequency 32 .

Therefore , Modal class is 0 - 2 .

$\green{ \mathbb { \underline{\underline{MEDIAN : }}}}$

$\sf Median = l + \bigg (\frac{ \frac{n}{2} - cf }{f} \bigg) \times h$

Median class = 2 - 4

$\sf Therefore \begin{cases} \sf l = 2 \\ \\ \sf \frac{n}{2} = \frac{100}{2} = 50 \\ \\ \sf \: cf = 32 \\ \\ \sf f = 25 \\ \\ \sf h = 2 \end{cases}$

$\sf Median = 2 + \bigg (\frac{ 50 - 32}{25} \bigg) \times 2 \\ \\ \sf Median = 2 + \bigg (\frac{18}{25} \bigg) \times 2 \: \: \: \: \: \: \: \: \: \\ \\ \sf Median = 2 + \frac{18}{25} \times 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Median = 2 + \frac{36}{25} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Median = \frac{50 + 36}{25} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Median = \frac{86}{25} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Median = 3.44 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$