Multiple choice

The scores of $10$ students in a class test are given as $44,54,46,63,55,42,34,48,70,38$. Calculate the mean deviation about the median.

  1. $8.6$
  2. $6.6$
  3. $7.6$
  4. $8.8$
  5. $None\ of\ these$
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A Correct answer
Explanation

The sorted data is 34, 38, 42, 44, 46, 48, 54, 55, 63, 70. The median is (46+48)/2 = 47. The absolute deviations from 47 are 13, 9, 5, 3, 1, 1, 7, 8, 16, 23. The sum is 86. The mean deviation is 86/10 = 8.6.

AI explanation

First, arrange the scores in ascending order: 34, 38, 42, 44, 46, 48, 54, 55, 63, 70. The median of these 10 observations is the average of the 5th and 6th values, which is (46 + 48) / 2 = 47. The mean deviation about the median is the sum of absolute deviations from 47 divided by 10. The absolute deviations are 13, 9, 5, 3, 1, 1, 7, 8, 16, and 23, which sum to 86. The mean deviation is 86 / 10. The result is 8.6.

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