Question

Find the median of:
(i) 3, 11, 7, 2, 5, 9, 9, 2, 10
(ii) 9, 25, 18, 15.6, 16, 8, 22, 21
(iii) 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22​

Answer 1

Step-by-step explanation:

(i) 5, 7, 9, 11, 15, 17, 2, 23 and 19

Arranging in ascending order : 2, 5, 7, 9, 11, 15, 17, 19, 23

Here, number of terms = 9 which is odd

Median = (n + 1)/2 = (9 + 1)2 th term = 5th term = 11

Hence, median = 11

(ii) 9, 3, 20, 13, 0, 7 and 10

Arranging in ascending order: 0, 3, 7, 9, 10, 13, 20

Here, number of terms = 7 which is odd

∴ Median = (n + 1)/2 = (7 + 1)/2 th term = 4th term = 9

Hence, median = 9

(iii) 18, 19, 20, 23, 22, 20, 17, 19, 25 and 21

Arranging in ascending order: 17, 18, 19, 19, 20, 20, 21, 22, 23, 25

Here, numbers of terms = 10 which is even.

∴ Median = 1/2 {n/2 th term + (n/2 +1) th term}

= 1/2 {10/2 th term + (10/2 +1) th term}

= 1/2{5th term + 6th term}

= 1/2 {20 + 20} = 1/2 × 20 = 20

Hence, median = 20

(iv) 3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9 and 7.6

Arranging in ascending order: 1.9, 2.7, 3.6, 3.8, 5.6, 6.5, 7.6, 8.9, 9.4, 10.8, 15.6

Here, number of terms = 11 which is odd

∴ Median = (n + 1)/2 = (11 + 1)/2 = 6th term

= 6th term = 6.5

Hence, median = 6.5