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| Math Central | Quandaries & Queries |
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Question from Reggie: After you have computed the standard deviation of a set of 40 scores, you discover that the lowest score is in error and should be even lower. Will correcting this error affect the standard deviation? |
Reggie,
The standard deviation measures the spread of the data so increasing the spread should increase the standard deviation. Here is a small example with easy numbers. (You should check my calculations.)
Suppose you have 3 scores, 1, 2 and 3. The sample mean is 2 and the standard deviation is 1. Suppose now you notice that the smallest score should be -2. The data is now -2, 2 and 3. The mean is 1 and the standard deviation is √14.
I hope this helps,
Penny
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