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Set rules - please add any that you may know

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Set rules - please add any that you may know

by netigen » Sun May 18, 2008 4:17 pm
Range rules
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Range = largest-smallest number in the set

1. If set has any negative number then range is > the largest number in the set
2. If set has all +ve numbers then range < largest number in the set

Median rules
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Median = middle value of an ordered set

1. Median of a set of odd number of terms will be a set value
2. Median of an even number of terms will not be a set value
3. Median=Mean in case of a set with equal distribution (1,2,3,4) or (2,5,8,11,14)

Mean rules
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Mean = average value of the set = sum of all values/n

n=number of terms

1. If Mean of a set with consecutive numbers is integer than n = odd
2. If Mean of a set with consecutive numbers is not integer than n = even
3. Sum of a set = mean x n

Standard deviation
-----------------------

1. If the SD of a set is known and the set numbers in the set are increased or decreased by same percentage/factor then the new SD can be calculated by just knowing the percentage/factor change.
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by luvaduva » Tue May 20, 2008 4:50 pm
Combined sets

Mean- The mean of set C combined from the two sets A and B will have a mean that lies between the two means of A and B or equal to both the means of sets A and B.

Median- The median of set C combined from the two sets A and B will have a median that lies between the two medians of A and B or equal to one or more of the medians of sets A and B.
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by netigen » Mon May 26, 2008 11:13 am
1. Mean Average = total of quantities / number of quantities
2. The median is the "middle" number in a group (when arranged in ascending or descending order) consisting of an odd number of numbers, and the average of the two middle numbers if there are an even number of numbers
3. For a set of consecutive integers, the median is the the average of the first and the last integer
4. Mode is the most frequently recurring number/numbers among the given set of numbers. It can be more than one
5. Range is the difference between the largest number and smallest number is a set
6. Calculation of Standard Deviation (SD):
i) Find the mean of the set of numbers
ii) Find the difference between each of the numbers and the mean
iii) Square the differences and add them together
iv) Take the positive square root of this value
7. Variance is the square of the standard deviation
8. SD does not change when the same constant is added or subtracted to all the members of the set
9. If mean = maximum value it means that all values are equal and SD is 0
10. 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
11. 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
12. SD is the square root of the average of the sum of square of the variation from the mean
13. The more uneven members are dispersed around their arithmetic average, the more their SD
14. You only need to know the difference between values and total number of values to compute SD
15. If we know all the numbers of the list, there is a definite SD, regardless of what it is, we can compute it and get an answer – this is helpful for DS questions
16. If the range is 0, then the SD must also be 0, because there is no variance
17. 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
18. The sum of the deviations of the elements from the mean must be 0
19.Closer the more values to the MEAN, lower the SD
20. If Range or SD of a list is 0, then the list will contain all identical elements
21. For data with approximately the same mean, the greater the range, the greater the SD
22. If you multiply all terms by x then SD =x times old SD and mean = x times old mean
23. 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
24. 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
25. For a given set of consecutive even numbers.. mean = median
26. For odd number of consecutive integers median = mean
27. Good links for Normal Distribution:
https://www-stat.stanford.edu/~naras/jsm ... nsity.html https://davidmlane.com/hyperstat/z_table.html
https://www.integratedlearning.net/gmat/sample.asp
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by beeparoo » Tue May 27, 2008 1:02 pm
netigen wrote: 6. Calculation of Standard Deviation (SD):
i) Find the mean of the set of numbers
ii) Find the difference between each of the numbers and the mean
iii) Square the differences, add them together, then divide by the number of terms
iv) Take the positive square root of this value
Just wanted to add that little bit.

(Got confused by definition of Variance... Didn't know if variance was just the sum of the squared-differences, or if it was that DIVIDED by the number of terms...

Sandra[/b]
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