Find the mean deviation about the median for the following data set:
3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5.27
The mean deviation about the median is the average distance of the observations from the median: find the median, take each value’s distance from it (ignoring the sign), and divide their sum by the number of values.
The median (the middle value once the data are in order):
In ascending order: 3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21 (11 values)
The 6th value is the middle one, so the median is 9
Distances from 9:
6, 6, 5, 4, 2, 0, 1, 3, 9, 10, 12
Their sum is 58
Mean deviation (sum of distances divided by the number of values):
\(\displaystyle\frac{58}{11}=5.27\)