Question

When a set of data are arranged in an ascending order that has the observations 42, 38, 37, 31, k + 8, 2k - 20, 21, 2k - 1, 13, 5. Then the median of the given set of data is 25.5. Find the value of k.
1. 19
2. 21
3. 24
4. 27

Answer 1

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