Question

Calculate the mode of the following distribution:

Class	10 − 15	15 − 20	20 − 25	25 − 30	30 − 35
Frequency	4	7	20	8	1

Answer 1

Modal class is the class with the highest frequency
modal class is 20 - 25
lower limit of modal class i.e l = 20
class size i.e h = 5
frequency of modal class f₁ = 20
frequency of preceding class f₀ = 7
frequency of succeeding class f₂ = 8
Using the formula
mode = `l + (( f_1 − f_0)/(2f_1 − f_0 − f_2)) xx h`

Plugging the values in the formula we get
mode = `20 + ( 20 −7)/( 2 × 20 − 7 − 8) xx 5`

mode = `20 + (13)/(25) xx 5`

mode = `20+13/5`

mode = `113/5` = 22.6