Correct Answer - Option 2 : 21
Given:
Data = {42, 38, 37, 31, k + 8, 2k - 20, 21, 2k - 1, 13, 5}
Median = 25.5
Number of observations = 10
Formula used:
If the total number of observations (n) is an odd number,
Median = (n + 1)/2th term
If the total number of observations (n) is an even number,
Median = {(n/2)th term + [(n/2) + 1]th term}/2
Calculations:
Arranging the values in ascending order,
5, 13, 2k - 1, 21, 2k - 20, k + 8, 31, 37, 38, 42
∵ The number of observations is even (i.e. 10)
Median = {(10/2)th term + [(10/2) + 1]th term}/2
⇒ {5th term + 6th term}/2
⇒ (2k - 20 + k + 8)/2 = 25.5
⇒ 3k - 12 = 51
⇒ 3k = 63
⇒ k = 21
∴ The value of k is 21