Question

Calculate mode of the following distribution:

Class	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35
Frequency	5	6	15	10	5	4

Answer 1

Maximum frequency (f₁) = 15

Class Corresponding to f₁ = 15 - 20

Modal class = 15 - 20

l = 15

h = 20 − 15 = 5

f₀ = 6

f₂ = 10

∴ Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

= `15 + ((15 - 6)/(2 xx 15 - 6 - 10)) xx 5`

= `15 + (9/(30 - 6 - 10)) xx 5`

= `15 + 9/14 xx 5`

= `15 + 45/14`

= 15 + 3.21

= 18.21 (approx.)