Find the median of the following data.

(i) 18,12,51,32,106,92,58

(ii) 28,7,15,3,14,18,46,59,1,2,9,21

(i). Let us arrange the numbers in ascending order. (Without arranging the values in ascending/descending order, we will not be able to get the correct median) We have,

12, 18, 32, 51, 58, 92 ,106 …(1)

Total number of items, n = 7 (odd number).

When n is odd, median is given by

⇒

⇒

⇒ Median = 4^th term

Count 4^th term from the arranged numbers in (1).

The 4^th term = 51

⇒ Median = 51 [∵ Median = 4^th term]

Thus, median is 51.

(ii). Let us arrange the numbers in ascending order. (Without arranging the values in ascending/descending order, we will not be able to get the correct median) We have,

1, 2, 3, 7, 9, 14, 15, 18, 21, 28, 46, 59 …(1)

Total number of items, n = 12 (even number).

When n is even, median is given by

⇒

⇒ Median = mean of 6^th and 7^th term

Count 6^th and 7^th term from the arranged numbers in (1).

The 6^th term = 14

& 7^th term = 15

⇒ Median = mean of 14 and 15 …(2)

Mean of 14 and 15 is calculated as,

⇒

Put mean of 14 and 15, 14.5 in equation (2),

Median = 14.5

Thus, median is 14.5.