Question

For the following data showing weights of 100 employees, find the maximum weight of the lightest 25% of employees.

Weight (kg)	45 – 50	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80
No. of employees	6	8	15	26	20	14	11

Answer 1

We construct the less than cumulative frequency table as given below:

Weight (kg)	No. of employees  (f)	Less than cumulative frequency  (c.f.)
45 – 50	6	6
50 – 55	8	14
55 – 60	15	29 ← Q1
60 – 65	26	55
65 – 70	20	75
70 – 75	14	89
75 – 80	11	100
Total	N = 100

Here, N = 100
Q₁ class = class containing `("N"/4)^"th"` observation

∴ `"N"/4 = 100/4` = 25

Cumulative frequency which is just greater than (or equal) to 25 is 29.

∴ Q₁ lies in the class 55 – 60.
∴ L = 55, h = 5, f = 15, c.f. = 14

∴ Q₁ = `"L" + "h"/"f" ("N"/4 - "c.f.")`

= `55 + 5/15 (25 - 14)`

= `55 + 1/3 xx 11`

= 55 + 3.67
= 58.67
∴ Maximum weight of the lightest 25% of employees is 58.67 kg.