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:

1. Median
2. Lower quartile
3. Upper quartile
4. Inter-quartile range

Answer 1

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)`

= 10^th 

= 29

ii. Lower quartile (Q₁) = `((n + 1)/4)^(th)`

= `((19 + 1)/4)^(th)`

= 5^th

= 26

iii. Upper quartile (Q₃) = `((3(n + 1))/4)^(th)`

= `((3(19 + 1))/4)^(th)`

= 3 × 5^th 

= 15^th

= 35

iv. Inter-quartile range = Q₃ – Q₁

= 35 – 26

= 9