Multiple choice

For a series of 5 numbers, the mean is 20, the median and mode are both 10, the highest number in the series is 50 and one of the numbers is 20. Find the number of times the modal value appears in the series.

  1. 4

  2. 1

  3. 2

  4. 3
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D Correct answer
Explanation

With 5 numbers, mean 20 implies sum = 100. Numbers are {x1, x2, x3, x4, x5}. Median is 10, so the third number is 10. Mode is 10, so at least two numbers must be 10. We have {x1, x2, 10, x4, 50}. Since the mode is 10, 10 must appear more than once. If 10 appears twice, the sum is x1 + x2 + 10 + 10 + 50 = 100, so x1 + x2 = 30. If 10 appears three times, the set is {x1, 10, 10, 10, 50}, sum = 80 + x1 = 100, so x1 = 20. This fits all conditions.

AI explanation

Since the mode is 10 and the median is 10, the ordered series must have 10 in the middle position. Because the mode is the most frequent number and we know one number is 20 and the highest is 50, the series must be arranged to have multiple 10s at the beginning. The series is 10, 10, 10, 20, 50, which satisfies the mean (sum is 100, mean is 20), the median (third value is 10), and the mode (10 appears most frequently). Therefore, the modal value of 10 appears 3 times in the series.

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