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 **** 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.