What is the mean of the median, mode and range for the data given below? 11,…
2019
What is the mean of the median, mode and range for the data given below?
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11, 9, 24, 25, 29
- A.
31
- B.
32
- C.
33
- D.
34
Attempted by 1 students.
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Correct answer: C
Median is the value at the middle position of a data set arranged in ascending order (for an odd count of n values, that position is (n + 1) / 2). Mode is the value occurring with the highest frequency, and range is the difference between the maximum and minimum values. When asked for the mean of these three descriptive statistics, first compute each one from the sorted data, then average the three results.
Sort the seventeen given values in ascending order: 0, 8, 9, 11, 11, 17, 18, 20, 24, 25, 25, 25, 29, 30, 30, 44, 50.
Locate the median: with n = 17 (odd), the median is the value at position (17 + 1) / 2 = 9, which is 24.
Identify the mode: 25 occurs three times in the list, more often than any other value, so the mode is 25.
Compute the range: subtract the minimum value from the maximum value, 50 minus 0, giving 50.
Average the three statistics: (24 + 25 + 50) divided by 3 equals 99 divided by 3, which equals 33.
Cross-check: adding the three values independently, 24 + 25 + 50 = 99, and 99 divided by 3 leaves no remainder, confirming the mean is exactly 33.