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What is the standard deviation of set X, containing

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What is the standard deviation of set X, containing  [#permalink]

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New post 13 Jun 2009, 15:33
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What is the standard deviation of set X, containing consecutive odd integers?

(1) Set consists of 10 elements
(2) The range of set is 18
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Re: What is the standard deviation of set X, containing  [#permalink]

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New post 13 Jun 2009, 23:57
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The answer is D.

Given: A set containing consecutive odd integers
Asking: The Standard Deviation.

Lets see..what do we need to find the standard deviation -- We need the difference between the average and each number in the set. We don't really care what the actual numbers are as long as we have the difference.

Lets look at Statement 1:
Set consists of 10 elements Sufficient. (will explain later)

Lets look at Statement 2:
The range of set is 18.
Which means the last number - first number = 18. We know that the difference between each consecutive integer is 2. We can use this to find out the number of elements in the set.

If the first number is n, then the second number is n+2, and third is n+4 and so on. The set will look like this

n,n+2,n+4,n+6,n+8,n+10,n+12,n+14,n+16,n+18
As (n+18) - n =18 we have defined all the numbers in the set..and if you count them it is 10.

So statement 2 is basically telling us the same thing that the Set consists of 10 elements. Hence Sufficient. (See reason below)

Now we know two things
1. The set has 10 elements
2. The numbers in the set are consecutive odd integers.

First we need to calculate the mean of these integers. Lets look at the set again as we described earlier:

n,n+2,n+4,n+6,n+8,n+10,n+12,n+14,n+16,n+18

The mean of a set of evenly spaced integers is
\(\frac{\text{First Integer}+\text{Last Integer}}{2}\)

\(= \frac{n+(n+18)}{2}\)

\(= \frac{2n+18}{2)\)

\(=n+9\)

Now that we know the mean we can find the difference between each integer in the set and the mean.

n-(n+9)=-9
(n+2)-(n+9)=-7
(n+4)-(n+9)=-5
(n+6)-(n+9)=-3
(n+8)-(n+9)=-1
(n+10)-(n+9)=1
(n+12)-(n+9)=3
(n+14)-(n+9)=5
(n+16)-(n+9)=7
(n+18)-(n+9)=9

This is all we need to calculate the SD. Hence both statements are sufficient.
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Re: What is the standard deviation of set X, containing  [#permalink]

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New post 14 Jun 2009, 00:21
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Standard deviation of consecutive odd integers depends only on the number of integers and doesn't depend on absolute values of the integers because SD is the deviation from an average.

1) It directly points out the number of integers. Sufficient.
2) range is also unambiguously points out the number of integers. Sufficient.

So, D
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Re: What is the standard deviation of set X, containing  [#permalink]

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New post 14 Jun 2009, 11:12
pmal04 wrote:
What is the standard deviation of set X, containing consecutive odd integers?

1) Set consists of 10 elements
2) The range of set is 18



Anytime, to find standard Deviation, if know number of integers and the difference between mean and each number in set, will find SD..
So both 1 and 2 provides enough information.
D is best
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Re: What is the standard deviation of set X, containing  [#permalink]

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New post 11 Apr 2019, 09:57
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Re: What is the standard deviation of set X, containing   [#permalink] 11 Apr 2019, 09:57
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