Question

Rishi's MAD
Here is Rishi's data.2,5,5,5,6,7



You said the MAD of Rishi's data is greater than 2
2.



Calculate the MAD.



Use paper if it helps you organize your thinking

Answer 1

First decide which MAD you mean. Two common meanings:

- Mean absolute deviation (average of absolute deviations from the mean)
- Median absolute deviation (median of absolute deviations from the median)

Compute both for Rishi's data: 2, 5, 5, 5, 6, 7.

1) Mean = (2+5+5+5+6+7)/6 = 30/6 = 5.
Absolute deviations from the mean: |2−5|=3, |5−5|=0, |5−5|=0, |5−5|=0, |6−5|=1, |7−5|=2.
Sum = 3+0+0+0+1+2 = 6. Mean absolute deviation = 6/6 = 1.

2) Median = (3rd+4th)/2 = (5+5)/2 = 5.
Absolute deviations from the median are the same set: {3,0,0,0,1,2}, sorted {0,0,0,1,2,3}.
Median of those (average of 3rd and 4th) = (0+1)/2 = 0.5.

So:
- MAD (mean absolute deviation) = 1.
- MAD (median absolute deviation) = 0.5.

If you meant the usual school definition (mean absolute deviation), the correct value is 1.