STANDARD DEVIATION : Calculation of Standard Deviation (SD)

Question

STANDARD DEVIATION :

Calculation of Standard Deviation (SD)

It is very unlikely that a GMAT problem will involve calculating the SD of a given series.

SD =x times old SD

mean = x times old mean

RANGE

MODE

Mode is the most frequently recurring number/numbers among the given set of numbers. It can be more than one

MEAN AND MEDIAN

https://www.integratedlearning.net/gmat/sample.asp

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Thanks Ian for pointing out the mistakes.

Guys, Please add if i missed something.

subarao · Answer

Thanks amitdgr for the info.
+1 for you

dk94588 · Answer

yes statistics class is all coming back to me now. it was only last year tho lol. thanks for the info although I'm pretty sure you don' t need to have advanced knowledge of stats for the GMAT, do you? It does kind of help you understand your score report tho.....

IanStewart · Answer

Step iii) above is not quite right- you want to take the mean of the squares, not the sum.

IanStewart · Answer

In 11: this could be confusing. A set such as {0,0,0,0, 1000000, 1000000, 1000000, 1000000} contains numbers which are very much 'alike' but the set has a huge standard deviation: all of its elements are very far from the mean.

In 13: I'm not exactly sure what you're trying to say here.

In 21: This is not a mathematical rule; indeed it's very often untrue. The set S = {100, 50, 50, 50, 50, 50, 50, 50, 0} has the same mean as the set T = {99, 99, 99, 99, 99, 99, 1, 1, 1, 1, 1, 1}, and has a larger range. It has a much smaller standard deviation, however.

In 26. For any number of consecutive integers, median = mean. You can remove the word 'odd'. Indeed, in any arithmetic progression, the median = mean.

amitdgr · Answer

Thanks Ian .. I guess I mistook some of the concepts

icandy · Answer

Thanks man. Into my book marks.

eresh · Answer

Thanks very much for the effort....however, do we need this sort of stat knowledge for GMAT?

GMAT888 · Answer

Thanx for the this useful stuff!!!

neomax85 · Answer

shortcut**

S.D=Sq.root(mean of the squares-square of the mean)

amod243 · Answer

Thank you so much amitdgr!!

pleonasm · Answer

Good compilation .. Thanks dude

eresh · Answer

Typo.........Should be divided by 2........

vannu · Answer

Could you explain how this verbatim would affect the below problem?

A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the followig pairs of data, when added to the list must result in a ist of 102 data with the standard deviation less than d?

Answer choices -

1. 0 and 6
2. 0 and 12
3. 0 and 0
4. -6 and 0
5. 6 and 6

Thanks,
Vannu

eresh · Answer

It is totally Ok. Welcome.

h2polo · Answer

Great post!

Just out of curiousity... has anyone actually seen a standard deviation problem in the real thing?

ctrlaltdel · Answer

Tip1.
Always keep in mind:
 Range >= SD >=0

Case1: when the set of numbers given are +ve and different: 2 3 4 : Range = 2, SD = sq-root (2/3). R > SD
Case2: when the set of numbers given are -ve and different: -4 -3 -2 : Range = 2, SD = sq-root (2/3). R > SD
Case3: Only in case of all numbers are equal, then Range = SD = 0, already mentioned above.

There cud be a problem where you are asked to arrange the Mean, median, mode, range & SD, any of these in ascending order. or framed differently for DS questions.

Tip2:
 Set of consecutive integers has mean 0, means set is symmetric about the origin. And yes # of terms should be odd. Thanks Bunuel 
 Case1: either all numbers are zero 
 Case2: or there are odd number of integers 
Helpful for DS again.

Kudos if you like the tips. More to come.........

Thanks Bunuel, edited the post as advised by you

Bunuel · Answer

I think it's not true. If set is for example: {1,1,1,5,7}
Mean=3
Median=1
Mode=1

And equation doesn't hold true. Check the source.

If we have set of  consecutive integers  how can all numbers be zero?

Set of consecutive integers has mean 0, means set is symmetric about the origin. And yes # of terms should be odd.

ctrlaltdel · Answer

Sorry for the confusion :oops:

Bunuel · Answer

This is about the special kind of distribution which you never see on GMAT.

Again if set is for example: {1,1,1,5,7}
Mean=5
Median=1
Mode=1

Put these values in the formula in red. You'll see the equation won't hold true.

I wouldn't advise to study this source in GMAT preparation.

STANDARD DEVIATION : Calculation of Standard Deviation (SD)

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