Multiple choice

Ten observations 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34 and 43 are written in ascending order. The median of the data is 24. What is the value of x?

  1. 15

  2. 18

  3. 20

  4. 24
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C Correct answer
Explanation

There are 10 observations. The median is the average of the 5th and 6th terms. 5th term = x + 1, 6th term = 2x - 13. Median = ((x + 1) + (2x - 13)) / 2 = 24. (3x - 12) / 2 = 24. 3x - 12 = 48. 3x = 60. x = 20.

AI explanation

For 10 observations in ascending order, the median is the average of the 5th and 6th terms. The 5th term is x + 1 and the 6th term is 2x - 13. Setting their average to 24 gives the equation (x + 1 + 2x - 13) / 2 = 24. Solving 3x - 12 = 48 yields x = 20.

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