Why Standard Deviation is Generally better than Range

Daniel F. Moore

Four Different Sets of Data

Run A Run B Run C Run DAverage 454.665 455.112 454.205 457.357Range 42.1380 41.8154 42.8437 44.1127

• Four all the sets, the average and the range are about the same

• So, the data sets are all almost the same, right?

Four Different Sets of Data

• No!!!• In fact, they are

extremely different in their shape and in what they might reveal about the underlying process

Four Different Sets of DataRun A Run B Run C Run D

Average 454.665455.1128454.2057457.3572Range 42.1380441.8154242.8437144.11273StDev 4.90950312.13244 6.559169.024437Max 487.9789 476.95487.9542487.2352Min 445.8409435.1346445.1105443.1225

• Let’s look further• Oh! They all have

very different standard deviations!

• Had we looked at this in the beginning we would have known that they were different

Four Different Sets of DataRun A Run B Run C Run D

Average 454.665455.1128454.2057457.3572Range 42.1380441.8154242.8437144.11273StDev 4.90950312.13244 6.559169.024437

• Run A and Run B have the same range and the same average, but they are very different from each other

• Quantitatively, this shows up in the standard deviation

Four Different Sets of DataRun A Run B Run C Run D

Average 454.665455.1128454.2057457.3572Range 42.1380441.8154242.8437144.11273StDev 4.90950312.13244 6.559169.024437Max 487.9789 476.95487.9542487.2352Min 445.8409435.1346445.1105443.1225

• So, if your goal is to determine how close your values are to the average, which measure should you use – standard deviation or range?

• Range is very susceptible to corruption by one data point– This corruption could be a measurement error or some other random

fluctuation that doesn’t correspond to normal process variation– If you need to enclose 100% of your values and don’t care about this type of

corruption, then range is partially what you want, but it won’t tell you anything about the shape of the data or the quality of your process