Question

If mode of the following frequency distribution is 55, then find the value of x.

Class	0 – 15	15 – 30	30 – 45	45 – 60	60 – 75	75 – 90
Frequency	10	7	x	15	10	12

Answer 1

Given: Mode of frequency distribution = 55

So, modal class is 45 – 60

Lower limit (l) = 45

Class interval (h) = 15

Also, `f_0` = 15, `f_1` = x and `f_2` = 10

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

⇒ 55 = `45 + ((15 - x)/(30 - x - 10)) xx 15`

⇒ 55 – 45 = `(15(15 - x))/(30 - x - 10)`

⇒ 10(30 – x – 10) = 225 – 15x

⇒ 300 –10x – 100 = 225 – 15x

⇒ 5x = 25

⇒ x = 5