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Question
The marks obtained by 19 students of a class are given below:
27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28.
Find:
- Median
- Lower quartile
- Upper quartile
- Inter-quartile range
Solution
Arranging in ascending order:
22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 31, 32, 32, 33, 35, 35, 36, 36, 37
i. Median = `((n + 1)/2)^(th)` term
= `((19 + 1)/2)^(th)`
= `(20/2)^(th)`
= 10th
= 29
ii. Lower quartile (Q1) = `((n + 1)/4)^(th)`
= `((19 + 1)/4)^(th)`
= 5th
= 26
iii. Upper quartile (Q3) = `((3(n + 1))/4)^(th)`
= `((3(19 + 1))/4)^(th)`
= 3 × 5th
= 15th
= 35
iv. Inter-quartile range = Q3 – Q1
= 35 – 26
= 9
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