Question

Calculate the median of the following distribution:

Weight (in nearest kg.)	No. of students
46	7
48	5
50	8
52	12
53	10
54	2
55	1

Answer 1

The given variates (weights of students) are already in ascending order. We construct the cumulative frequency table as under:

Variable (weight)	Frequency (No.of Students)	Cumulative frequency
46	7	7
48	5	12
50	8	20
52	12	32
53	10	42
54	2	44
55	1	45

Here, n = 45, which is odd.
∴ Median = `("n" + 1)/(2)`th observation
= 23^rd observation = 52.
(∵  All observation from 21^st to 32^nd are equal, each = 52).