(a) Find the median of the following set of numbers : 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7 (1990) (b)For the following set of numbers, find the median: 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15.
(a) Find the median of the following set of numbers : 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7 (1990) (b)For the following set of numbers, find the median: 10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15.

Solution:

(a) Arranging the numbers in ascending order :

0, 1, 2, 2, 3, 4, 5, 5, 5, 7, 8, 9

Here, n = 12 which is even

Median = ½ ( n/2 th term + ((n/2)+1)th term)

= ½ (12/2 th term + ((12/2)+1)th term)

= ½ (6 th term + (6+1)th term)

= ½ (6 th term + 7th term)

= ½ (4+5)

= 9/2

= 4.5

Hence the median is 4.5.

(b) Arranging the numbers in ascending order :

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81

Here, n = 12 which is even

Median = ½ ( n/2 th term + ((n/2)+1)th term)

= ½ (12/2 th term + ((12/2)+1)th term)

= ½ (6 th term + (6+1)th term)

= ½ (6 th term + 7th term)

= ½ (15+17)

= ½ ×32

= 16

Hence the median is 16.