Question

Find mode for given data:

Class	20-29	30-39	40-49	50-59	60-69
Frequency	15	20	50	30	10

Answer 1

Class	20 - 2920−2	30 - 39	40 - 4940−49	50 - 5950−59	60 - 69
Class Boundaries	19.5 - 29.5	29.5 - 39.5	39.5 - 49.5	49.5 - 59.549.5−59.5	59.5 - 69.5
Frequency	15	20	50	30	10

For the given data, Modal Class(Class with highest frequency) $=39.5-49.5$

For the modal class

l$=$ lower limit of modal class $=39.5$

h$=$ size of class interval $=10$

$f_1=$ frequency of modal class $=50$

$f_0=$ frequency of class preceding modal class $=20$

$f_2=$ frequency of class succeeding modal class $=30$

$Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$Mode=39.5+\frac{50-20}{(2\times 50)-20-30}\times 10$

$Mode=39.5+\frac{30}{50}\times 10$

$Mode=45.5$