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Question
The median of the following observations arranged in ascending order is 24. Find x:
11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41.
Solution
11, 12, 14, 18, x + 2, x + 4, 30, 32, 35
n = 10 (even), Median = 24
∴ Median = `(("n"/2)^"th" "term" + ("n"/2 + 1)^"th" "term")/(2)`
= `((10/2)^"th" "term" + (10/2 + 1)^"th" "term")/(2)`
Median = `(5^"th" "term" + 6^"th" "term")/(2)`
24 = `(x + 2 + x + 4)/(2)`
2x + 6 = 24 x 2
⇒ 2x = 48 - 6
⇒ 2x = 42
x = 21.
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