Question

Find the mode of the following frequency distribution:

Class:	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency:	25	30	45	42	35

Answer 1

Since, class 40 – 50 have highest frequency.

So, modal class is 40 – 50.

Lower limit (l) of modal class = 40

Class size (h) = 10

Frequency of modal class (f₁) = 45

Frequency of class proceeding to modal class (f₀) = 30

Frequency of class succeeding to modal class (f₂) = 42

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

= `40 + ((45 - 30)/(90 - 30 - 42)) xx 10`

= `40 + 150/18`

= `(720 + 150)/18`

= `870/18`

= 48.33