Multiple choice

15, 14, 18, 17, x The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of x ?

  1. 6

  2. 11

  3. 16

  4. 21
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A Correct answer
Explanation

Numbers: 14, 15, 17, 18, x. Mean = (64+x)/5. Median depends on x. If x is small, median is 15 or 17. If x=6, set is 6, 14, 15, 17, 18. Median=15. Mean=(64+6)/5 = 14. 14 != 15. If x=11, set is 11, 14, 15, 17, 18. Median=15. Mean=(64+11)/5 = 15. 15=15. If x=16, set is 14, 15, 16, 17, 18. Median=16. Mean=(64+16)/5 = 16. 16=16. If x=21, set is 14, 15, 17, 18, 21. Median=17. Mean=(64+21)/5 = 17. 17=17. Only x=6 fails.

AI explanation

The sum of the four known numbers is 64, so the overall mean is the quantity x plus 64, all divided by 5. We evaluate the median for the possible values of x by ordering the set. When x is 11, the set is 11, 14, 15, 17, 18 and both the median and mean are 15; when x is 16 or 21, the median is 16 and the mean also evaluates to 16. However, if x is 6, the ordered set is 6, 14, 15, 17, 18, making the median 15, but the mean becomes 14, so the values are not equal.

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