Question

The following data has been arranged in ascending order.
0, 1, 2, 3, x + 1, x + 5, 20, 21, 26, 29.
Find the value of x, if the median is 5.

Answer 1

Data in ascending order:
0, 1, 2, 3, x + 1, x + 5, 20, 21, 26, 29.
Here, total number of observation = n = 10 (even)
Median = 5

⇒ `(("n"/2)^"th" "term" + ("n"/2 + 1)^"th" "term")/(2)` = 5

⇒ `(5^"th" "term" + 6^"th" "term")/(2)` = 5

⇒ `((x + 1) + (x + 5))/(2)` = 5

⇒ 2x + 6 = 10
⇒ 2x = 4
⇒ x = 2.