Standard Deviation----Resolved

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Read about these rules related to Standard Deviation in one of the forums. Sharing it for the benefit of the group:

Source link mentioned below:

Some useful SD related notes I made:

1. Calculation of Standard Deviation (SD):
* Find the mean of the set of numbers
* Find the difference between each of the numbers and the mean
* Square the differences and add them together
* Take the positive square root of this value

2. If you add/subtract a constant value K to/from all the numbers in a list, the arithmetic mean increases/decreases by K but the standard deviation remains the same.

3. If you multiply/divide all the numbers in the list by a constant value K, both the arithmetic mean and the standard deviation are multiplied/divided by K.

4. If mean = maximum value it means that all values are equal and SD is 0

~~5. A set of numbers with range of zero means that all of the numbers are the same, hence the dispersion of the numbers from its mean is zero~~

6. SD ranks the dispersion (deviation) of the numbers in a list. The more alike the numbers are, the less the dispersion, so the less the standard deviation. The more uneven members are dispersed around their arithmetic average, the more their SD

7. If the range is 0, then the SD must also be 0, because there is no variance

8. 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

9. Standard deviation is how far the values spread out from the mean. A regular Bell Curve will always have 68% of the values within 1 SD, 95% of them within 2 SDs, and 99.7% within 3 SDs.High SD means the values are spread out; small SD means they're clustered closely around the mean.
... for more details: https://www.urch.com/forums/gmat-prob...uestion-2.html (Baffling standard deviation question)

10. For comparing the SD for two sets any information about mean ,median,mode and range are insufficient unless you can determine the individual terms from the given data

https://www.urch.com/forums/gmat-proble ... ation.html

...thanks to the original author

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roopPreps · Answer

edited point no 5...i felt it was not correct

roopPreps · Answer

REDUCE SD:.
 by adding numbers that are closer to the mean than are any of the existing numbers.
INCREASE SD:
 by adding numbers that are farther from the mean than are any of the existing numbers

Standard Deviation----Resolved

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