Multiple choice

Find the mean deviation from the median for the following ungrouped data $20, 25, 30, 18, 15, 40$

  1. $6$
  2. $4$
  3. $7$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Data: 15, 18, 20, 25, 30, 40. Median = (20 + 25) / 2 = 22.5. Mean deviation = (|15-22.5| + |18-22.5| + |20-22.5| + |25-22.5| + |30-22.5| + |40-22.5|) / 6 = (7.5 + 4.5 + 2.5 + 2.5 + 7.5 + 17.5) / 6 = 42 / 6 = 7.

AI explanation

First, arrange the data in ascending order: 15, 18, 20, 25, 30, 40. The median is the average of the two middle values: (20 + 25) / 2 = 22.5. The absolute deviations from the median are 7.5, 4.5, 2.5, 2.5, 7.5, and 17.5. The sum of these absolute deviations is 42, and dividing by the total number of observations gives the mean deviation: 42 / 6 = 7. The mean deviation from the median is 7.

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