Question

The following is the frequency distribution with unknown frequencies : 

Class	60-70	70-80	80-90	90-100	Total
frequency	`"a"/2`	`(3"a")/2`	2a	a	50

Find the value of a, hence find the frequencies. Draw a histogram and frequency polygon on the same coordinate system.

Answer 1

Total frequency = 50

∴ `a/2 + (3a)/2 + 2a + a = 50`

⇒ `(a + 3a + 4a + 2a)/2 = 50`

⇒ `(10a)/2 = 50`

⇒ `a = (50 xx 2)/10`

⇒ a = 10

∴ `a/2 = 10/2 = 5`

`(3a)/2 = (3 xx 10)/2 = 15`

2a = 2 × 20 = 40

a = 10

Hence the total would be represented as given below:

Class	60-70	70-80	80-90	90-100	Total
frequency	5	15	20	10	50