Standard Deviation

[abhiram guvvala]

Q A set has n integers.Average = M and SD= D.If int N is added the SD of new set is less than D .

 

Which of the following must be true??

 

 

a) N>M

b) N<M

c)N<D

 

Guys if an in is added to a set and the resulting SD is lower than that os the previous set then...the integer added is very close to Mean..

 

I know this rule ==> in the above options it could be both A and B.....hence N>M and N<M is out..

 

I didnt know how to interpret N<D....

 

 

Please help.....

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thanx and regards

[Kripa Tewari]

Hi Abhiram,

 

You are right in interpreting that N > M and N < M both are possible as when you take the SD you square the difference between mean and number. Hence option and a and b is out.

Now to your query..

if number is N < D meaning N is less than the maximum variation from mean. So untill and unless u expceep the maximum deviation your resulting SD will always less than previous one.

 

Example.. let us say SD is 2 in a set meaning maximum deviation any number in set can have is 2 from mean. if u add a number which is more than SD let us say 5 then ur SD will increase. Though otherway it will be less than D.

 

Hope you get the logic.

 

Regards

Kripa

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[Kripa Tewari]

one important point which u remember then can easily pick the answer without thinking all in detail.. " The more the data in a set is spread the more the standard deviation is".

[amith kumar]

Well done Kripa...that was a good explanation

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Rgds
Amith Ravindra