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Question
The weight of 60 boys are given in the following distribution table:
| Weight (kg) | 37 | 38 | 39 | 40 | 41 |
| No. of boys | 10 | 14 | 18 | 12 | 6 |
Find:
- Median
- Lower quartile
- Upper quartile
- Inter-quartile range
Solution
| Weight (kg) x |
No. of boys f |
Cumulative frequency |
| 37 | 10 | 10 |
| 38 | 14 | 24 |
| 39 | 18 | 42 |
| 40 | 12 | 54 |
| 41 | 6 | 60 |
Number of terms = 60
i. Median = The mean of the 30th and 31st terms
∴ Median = `(39 + 39)/2`
= `78/2`
= 39
ii. Lower quartile (Q1) = `60^(th)/4` term
= 15th term
= 38
iii. Upper quartile (Q3) = `(3 xx 60^(th))/4` term
= 45th term
= 40
iv. Inter-quartile range = Q3 – Q1
= 40 – 38
= 2
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