Median Absolute Deviation: Identify the Raw or Scaled Convention

The statistical question

The raw median absolute deviation is the median of absolute distances from the sample median. It measures spread in the original measurement units and is less influenced by extreme tail values than a standard deviation. Software may report a scaled version instead. The raw quantity and a distribution-consistency scaling are not the same definition, so the method belongs beside the value.

Primary reference: NIST Engineering Statistics Handbook.

An illustrative review example

For invented readings 8,9,10,11 and 20 mm, the median is 10 mm. Absolute distances from that median are 2,1,0,1 and 10 mm; their ordered middle value is 1 mm. That is the raw MAD for this illustration. Multiplying by a separately chosen scaling factor would produce another reported value. Neither calculation changes the actual 20 mm observation or proves that it is acceptable.

Prepare the evidence for discussion

Ask the analyst to record the center used, raw-versus-scaled convention, units and any distributional rationale for scaling. Do not compare two files labeled MAD until those definitions match. Keep the full distance calculation for a small check sample and the original measured values for engineering review. If the machine-trial criterion specifies standard deviation, a robust statistic cannot silently replace it without a revised agreement.

Raw distances and declared scaling

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• Primary reference: NIST Engineering Statistics Handbook