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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 |
Solution
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.
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