Multiple choice

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41. What is the mean deviation of the largest five observations?

  1. 4.8

  2. 5.5

  3. 6

  4. 7.5
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C Correct answer
Explanation

Sorted observations: 15, 18, 19, 21, 24, 32, 35, 41, 47, 50. Largest five: 32, 35, 41, 47, 50. Mean = (32+35+41+47+50)/5 = 205/5 = 41. Mean deviation = (|32-41| + |35-41| + |41-41| + |47-41| + |50-41|) / 5 = (9 + 6 + 0 + 6 + 9) / 5 = 30 / 5 = 6.

AI explanation

The largest five observations from the given data set are 35, 41, 47, 50, and 32, which when sorted become 32, 35, 41, 47, and 50. The arithmetic mean of these five observations is calculated as 32 plus 35 plus 41 plus 47 plus 50, yielding 205, and dividing by 5 gives a mean of 41. To find the mean deviation, calculate the absolute differences from the mean, which are 9, 6, 0, 6, and 9, and then find their mean by adding them to get 30 and dividing by 5, resulting in 6.

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