STANDARD DEVIATION : 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 take the mean of the differences (Thanks Ian) iv) Take the positive square root of this value It is very unlikely that a GMAT problem will involve calculating the SD of a given series. 1.SD does not change when the same constant is added or subtracted to all the members of the set. 2.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. In other words, If the range is 0, then the SD must also be 0, because there is no variance. 3.If Range or SD of a list is 0, then the list will contain all identical elements. 4.You only need to know the difference between values and total number of values to compute SD. 5.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. 6.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. 7.The sum of the deviations of the elements from the mean must be 0 8.Closer the more values to the MEAN, lower the SD 9.If you multiply all terms by x then SD =x times old SD and the mean = x times old mean 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. 11.If mean = maximum value it means that all values are equal and SD is 0. 12.Variance is the square of the standard deviation RANGE : 1. Range is the difference between the largest number and smallest number in a set 2. If Range of a list is 0, then the list will contain all identical elements. Or if a set contains all identical elements, then range = 0 3. If a set contains only one item, then range = 0 MODE : Mode is the most frequently recurring number/numbers among the given set of numbers. It can be more than one MEAN AND MEDIAN : 1. Arithmetic 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. For a given set of consecutive even/odd (or evenly spread) numbers mean = median 5. For a given set of consecutive integers median = mean https://www.integratedlearning.net/gmat/sample.asp ----------------------------------------------------------------------------------------------------------------- Thanks Ian for pointing out the mistakes. Guys, Please add if i missed something.

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STANDARD DEVIATION : Calculation of Standard Deviation (SD)

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ctrlaltdel

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17 Nov 2009, 14:18

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Thanks Bunuel.
Kudos for the timely monitoring.

From next time, i will PM you and confirm the tips before posting :oops:

Sorry for the confusion across the tips posted.

rongali

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thanks amitdgr for the info

BN1989

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04 Jan 2012, 05:54

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Could somebody elaborate on point 4?

I don't see how knowing the difference between the value and the total numbers of terms gives you the SD, or is it supposed to be the difference between the values and the mean?

skamran

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Bunuel

ctrlaltdel

Tip2:
There is a formula: (I don't know if it will be relevant for GMAT)
3*Median = 2*Mode + Mean
Helpful for DS.

I think it's not true. If set is for example: {1,1,1,5,7}
Mean=5
Median=1
Mode=1

Can you please explain how the mean is 5???

Bunuel

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05 Mar 2015, 08:55

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skamran

Bunuel

ctrlaltdel

Tip2:
There is a formula: (I don't know if it will be relevant for GMAT)
3*Median = 2*Mode + Mean
Helpful for DS.

I think it's not true. If set is for example: {1,1,1,5,7}
Mean=5
Median=1
Mode=1

Can you please explain how the mean is 5???

____
It's a typo , the mean is 3.

skamran

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05 Mar 2015, 08:58

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I think it's not true. If set is for example: {1,1,1,5,7}
Mean=5
Median=1
Mode=1

Can you please explain how the mean is 5???[/quote]
____
It's a typo , the mean is 3.[/quote]
Alright ...thanks for your quick response.

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Bunuel

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