Question

For the data given below find graphically the following :
(a) First and Third quartile
(b) The central 50% limit of the age .
(c) The number of workers falling in the age group of 28 to 57 years.

Age in years	:	20-24	25-29	30-34	35-39	40-44	45-49
No.of workers	:	5	10	15	25	65	40

Age in years	:	50-54	55-59	60-64	65-69
No.of workers	:	23	10	5	2

Answer 1

(a)
In order to find quartiles graphically, we first convert the inclusive series into exclusive series and then convert the frequency distribution into cumulative frequency distribution as follows:

Age	Age	Frequency (f)	Cumulative Frequency (c.f.)
19.5 – 24.5 24.5 – 29.5 29.5 – 34.5 34.5 – 39.5 39.5 – 44.5 44.5 – 49.5 49.5 – 54.5 54.5 – 59.5 59.5 – 64.5 64.5 – 69.5	Less than 24.5 Less than 29.5 Less than 34.5 Less than 39.5 Less than 44.5 Less than 49.5 Less than 54.5 Less than 59.5 Less than 64.5 Less than 69.5	5 10 15 25 65 40 23 10 5 2	5 15 30 55 120 160 183 193 198 200

Thus, the first and third quartiles are 38.5 and 48.25 respectively.

(b) The two limits (i.e. Q₁ and Q₃) with which central 50% of items lie are 38.5 and 48.25.

(c)


From the graph it is clear that total Number of workers of age 57 years = 190

Total Number of workers of age 28 years = 11
Number of workers falling in the age group of 28 to 57 years = 190 $-$11=179