MADNumbers to 50
Name: Date:
Find the mean absolute deviation of each set of numbers.
1
MAD16, 2, 8, 26, 8
2
MAD25, 5, 23, 17, 5
3
MAD1, 37, 39, 17, 1
4
MAD34, 34, 22, 18, 47
5
MAD32, 14, 45, 47, 32
6
MAD22, 22, 27, 31, 8
Mean absolute deviation worksheets
The mean says where a set of numbers sits; the mean absolute deviation says how spread out they are around it. These free printable worksheets ask for that spread, worked from a whole-number mean so the answer is always one clean decimal.
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Mean absolute deviation
The answer key prints on a separate page.
What's on this sheet
MAD is a mean of a mean, and saying it in that order is what makes it stick. First find the ordinary mean. Then, for each number, its distance from that mean — the size of the gap, with the sign thrown away, because a number three below is as far off as one three above. Then the mean of those distances. A child who tries to hold all three steps at once gets lost; a child who does them in order does not.
Why this sheet works
Every set here is built so the mean is a whole number, which is not a convenience but the thing that makes the sheet answerable. A mean absolute deviation is a fifth of a whole number, so it always lands on a single decimal place — 2.4, or 8, never 2.4666. A set of five free numbers would ask a sixth-grader for a repeating decimal with nowhere to write it, so the total is built to divide by five, the same backward construction the mean-median-mode sheets use.
How this one works
One question from this sheet, worked through a step at a time.
MAD of 16, 2, 8, 26, 8
1628268
mean =12
1628268
distance:4104144
distance:4104144
36 ÷ 5 =7.2
- The mean absolute deviation measures how spread out the numbers are. First find the mean: 16 + 2 + 8 + 26 + 8 = 60, then 60 ÷ 5 = 12.
- Now the distance of each number from 12, with the sign thrown away: 4, 10, 4, 14, 4.
- Then average those distances: 4 + 10 + 4 + 14 + 4 = 36, and 36 ÷ 5 = 7.2.