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Standard Deviation 10 Rules to Remember:
1. |Median-Mean| <= SD.
2. Variance is the square of the standard deviation.
3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.
4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).
5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.
6. If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change.
7. If we increase or decrease each term in a set by the same percent: Mean will increase or decrease by the same percent.SD will increase or decrease by the same percent.
8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.
9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.
10 If a series is in Arithmetic Progression then the series will have Mean = Median
1. |Median-Mean| <= SD.
2. Variance is the square of the standard deviation.
3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.
4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).
5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.
6. If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. SD will not change.
7. If we increase or decrease each term in a set by the same percent: Mean will increase or decrease by the same percent.SD will increase or decrease by the same percent.
8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.
9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.
10 If a series is in Arithmetic Progression then the series will have Mean = Median
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