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:

(i) Median

(ii) lower quartile

(iii) Upper quartile

(iv) Inter-quartile range

Arranging in ascending order:

22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 21, 32, 32, 33, 35, 35, 36, 36, 37

(i) Here, n = 19, which is odd.

By formula,

Median = $\dfrac{n + 1}{2}$ th term.

= $\dfrac{19 + 1}{2} = \dfrac{20}{2}$ = 10th term

= 29.

Hence, median = 29.

(ii) Since, n = 19, which is odd.

By formula,

Lower quartile = $\dfrac{n + 1}{4}\text{ th term} = \dfrac{19 + 1}{4} = \dfrac{20}{4}$

= 5th term = 26.

Hence, lower quartile = 26.

(iii) Since, n = 19, which is odd.

By formula,

Upper quartile = $\dfrac{3(n + 1)}{4}\text{ th term} = \dfrac{3(19 + 1)}{4} = \dfrac{3 \times 20}{4}$

= 15th term = 35.

Hence, upper quartile = 35.

(iv) Inter quartile range = Upper quartile - Lower quartile

= 35 - 26

= 9.

Hence, inter quartile range = 9.