Question

Ten students appeared for a test in Mathematics and Statistics and they obtained the marks as follows:

Sr. No.	1	2	3	4	5	6	7	8	9	10
Marks in Mathematics	42	38	36	32	23	25	35	37	25	23
Marks in Statistics	22	26	29	34	50	45	23	28	32	36

If the median will be the criteria, in which subject, the level of knowledge of the students is higher?

Answer 1

Marks in Mathematics can be arranged in ascending order as follows:
23, 23, 25, 25, 32, 35, 36, 37, 38, 42
Here, n = 10
∴ Median = value of `(("n"+1)/2)^"th"` observation

= value of `((10+1)/2)^"th"` observation

= value of (5.5)^th observation
= value of 5^th observation + 0.5 (value of 6^th observation – value of 5^th observation)
= 32 + 0.5 (35 – 32)
= 32 + 0.5(3)
= 32 + 1.5
= 33.5
Marks in Statistics can be arranged in ascending order as follows:
22, 23, 26, 28, 29, 32, 34, 36, 45, 50
Here, n = 10

∴ Median = value of `(("n"+1)/2)^"th"` observation

= value of `((10+1)/2)^"th"` observation

= value of (5.5)^th observation
= value of 5^th observation + 0.5 (value of 6^th observation – value of 5^th observation)
= 29 + 0.5 (32 – 29)
= 29 + 0.5(3)
= 29 + 1.5
= 30.5
∴ Median marks for Mathematics = 33.5
and Median marks for Statistics = 30.5
∴ The level of knowledge in Mathematics is higher than that of Statistics.