Use Mean Absolute Deviation to Compare Spread
Calculate the record’s mean, find each absolute distance from it, then average those distances.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Record A is 3,3,7,7 minutes.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Mean absolute deviation averages the distances from the mean. Distances are nonnegative, so values below the mean do not cancel values above it. Two records can have the same mean but different spread. A comparison should name the units, observation count, and supplied sample rather than claim all future cases will match.
Calculate the record’s mean, find each absolute distance from it, then average those distances. Compare with another record using the same units. Describe spread with evidence and state that the conclusion covers only the supplied observations.
Average distances rather than signed differences. A shared mean does not imply equal spread or identical distributions. Make columns for value, mean, and nonnegative distance, then average the final column.
- Make columns for value, mean, and nonnegative distance, then average the final column.
- Work through the supplied example and label what each number or attribute represents.
- Calculate the record’s mean, find each absolute distance from it, then average those distances.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
Record A is 3,3,7,7 minutes. Mean is five, and distances are 2,2,2,2, so MAD is two. Record B is 4,4,6,6 with the same mean five but MAD one. A is more spread in these four-observation records; the shared mean does not make their distributions identical. Average distances rather than signed differences. A shared mean does not imply equal spread or identical distributions. Make columns for value, mean, and nonnegative distance, then average the final column.
Check your reasoning
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Helpful tips
- Average distances rather than signed differences.
- A shared mean does not imply equal spread or identical distributions.
See the answer and explanation
3
With equal repeats of two values, the mean is their midpoint and each distance is half their difference. The result is 3.
Take it further
Compare 1,1,9,9 and 4,4,6,6. Expected mean five for both; MAD four versus one.
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