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Why standard deviation is generally better than range

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Why standard deviation is generally better than range

  1. 1. Why Standard Deviation is Generally better than Range Daniel F. Moore
  2. 2. Four Different Sets of Data <ul><li>Four all the sets, the average and the range are about the same </li></ul><ul><li>So, the data sets are all almost the same, right? </li></ul>Run A Run B Run C Run D Average 454.665 455.112 454.205 457.357 Range 42.1380 41.8154 42.8437 44.1127
  3. 3. Four Different Sets of Data <ul><li>No!!! </li></ul><ul><li>In fact, they are extremely different in their shape and in what they might reveal about the underlying process </li></ul>
  4. 4. Four Different Sets of Data <ul><li>Let’s look further </li></ul><ul><li>Oh! They all have very different standard deviations! </li></ul><ul><li>Had we looked at this in the beginning we would have known that they were different </li></ul>Run A Run B Run C Run D Average 454.665 455.1128 454.2057 457.3572 Range 42.13804 41.81542 42.84371 44.11273 StDev 4.909503 12.13244 6.55916 9.024437 Max 487.9789 476.95 487.9542 487.2352 Min 445.8409 435.1346 445.1105 443.1225
  5. 5. Four Different Sets of Data <ul><li>Run A and Run B have the same range and the same average, but they are very different from each other </li></ul><ul><li>Quantitatively, this shows up in the standard deviation </li></ul>Run A Run B Run C Run D Average 454.665 455.1128 454.2057 457.3572 Range 42.13804 41.81542 42.84371 44.11273 StDev 4.909503 12.13244 6.55916 9.024437
  6. 6. Four Different Sets of Data <ul><li>So, if your goal is to determine how close your values are to the average, which measure should you use – standard deviation or range? </li></ul><ul><li>Range is very susceptible to corruption by one data point </li></ul><ul><ul><li>This corruption could be a measurement error or some other random fluctuation that doesn’t correspond to normal process variation </li></ul></ul><ul><ul><li>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 </li></ul></ul>Run A Run B Run C Run D Average 454.665 455.1128 454.2057 457.3572 Range 42.13804 41.81542 42.84371 44.11273 StDev 4.909503 12.13244 6.55916 9.024437 Max 487.9789 476.95 487.9542 487.2352 Min 445.8409 435.1346 445.1105 443.1225

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