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# What is the variance of set X, which contains only consecutive even in

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What is the variance of set X, which contains only consecutive even in  [#permalink]

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29 Nov 2016, 00:45
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45% (medium)

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57% (01:02) correct 43% (01:13) wrong based on 131 sessions

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What is the variance of set X, which contains only consecutive even integers?

(1) X consists of 10 terms.

(2) The range of X is 18.

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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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29 Nov 2016, 01:30
Bunuel wrote:
What is the variance of set X, which contains only consecutive even integers?

(1) X consists of 10 terms.

(2) The range of X is 18.

Ans : A

I think we just need to know the how many terms are present, as the set contains consecutive even integers.
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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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29 Nov 2016, 03:25
Ans:D

For consecutive even integers the series would be 2n, 2n+2,2n+4... And so on
St 1: there are 10 terms thus each term will have 2n and it will get cancelled while calculating difference between mean and term thus SD can be calculated and variance is possible. Sufficient
St2: As the range is 18 and these are consequetive integers, no of terms would be 10 only. Thus same as St 1. Hence sufficient.

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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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29 Nov 2016, 21:00
1
Bunuel wrote:
What is the variance of set X, which contains only consecutive even integers?

(1) X consists of 10 terms.

(2) The range of X is 18.

IMO: D Please find the attachemnt
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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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04 Jan 2018, 15:13
Definition of Variance = The average of the squared differences from the Mean.

if the set = 1, 2, 3, 4 ,5 : variance = ($$(3-1)^2$$ + $$(3-2)^2$$ + $$(3-3)^0$$ + $$(3-4)^2$$ + $$(3-5)^2)$$/(5) = 2

As we can see that $$(3-1)^2$$ = $$(3-5)^2$$ & $$(3-2)^2$$ = $$(3-4)^2$$

so we need to know the mean of the set & the number of terms in the set.

statement 1 says : number of terms = 10

let's say first term a(1) = 2n ( since its given numbers are set of even consecutive numbers)
a(n) = a(1) + (n-1)d : d = common difference
a(n) = 2n + (10-1)* 2 = 2n + 18

so we have the set ,.. 2n, 2n+2, 2n+6,........2n+18

mean of the consecutive numbers = $$\frac{(first term + last term )}{2}$$ = 2n+ 18+2n/ 2 = 2n + 9

so we can calculate the variance as we do have the number of terms and mean of the set.

A is sufficient

statement 2: Range = 18

last term - first term = 18
last term - 2n = 18
last term = 2n + 18

we have the last term and we have the first term so we can find out the number of terms in the set.

hence we can find the variance too using this statement

hence this is also sufficient.

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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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15 Jan 2018, 02:40
vivekkumar987 wrote:
Bunuel wrote:
What is the variance of set X, which contains only consecutive even integers?

(1) X consists of 10 terms.

(2) The range of X is 18.

IMO: D Please find the attachemnt

thank for the explanation but no where in the problem it says that there are no repeated numbers

the set could also be

20 22 22 24 26 26 28

or 20 22 24 26 26 etc...

each have different variance so the answer could be E
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Posts: 52296
Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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15 Jan 2018, 04:16
coolnaren wrote:
vivekkumar987 wrote:
Bunuel wrote:
What is the variance of set X, which contains only consecutive even integers?

(1) X consists of 10 terms.

(2) The range of X is 18.

IMO: D Please find the attachemnt

thank for the explanation but no where in the problem it says that there are no repeated numbers

the set could also be

20 22 22 24 26 26 28

or 20 22 24 26 26 etc...

each have different variance so the answer could be E

20 22 22 24 26 26 28 and 20 22 24 26 26 do not represent consecutive even numbers.

Consecutive even integers mean even integers that follow each other in order with common difference of 2: ... x-6, x-4, x-2, x, x+2, x+4, ....
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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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15 Jan 2018, 06:29
Given: x=set(consecutive even integers)

ST1: x consists of 10 terms ---> x=set(10 consecutive even integers)
Clearly, the Standard deviation can be calculated and from this variance too.
ST1 ---> Sufficient

ST2: Range (x) = 18
From range rule, the range is approximately 4 times Standard deviation.
So, from ST2, the standard deviation can be estimated and from this variance too.
ST2 ---> Sufficient

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Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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30 Apr 2018, 05:08
there can also be a set {-2,0,2,4,6,8,10,12,14,16} range = 18
but the sd will vary.
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Posts: 52296
Re: What is the variance of set X, which contains only consecutive even in  [#permalink]

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30 Apr 2018, 05:25
failatmath wrote:
there can also be a set {-2,0,2,4,6,8,10,12,14,16} range = 18
but the sd will vary.

If we add or subtract a constant to each term in a set the standard deviation will not change.

A set of consecutive even integers, whose range is 18 consists of 10 terms: x, x+2, x+4, x+6, x+8, x+10, x+12, x+14, x+16, x+18 (where x is an even number). You can substitute any even number for x and all those sets will have the same standard deviation. For example, the SD of {-2, 0, 2, 4, 6, 8, 10, 12, 14, 16} is $$\sqrt{33}$$, so is the SD of {0, 2, 4, 6, 8, 10, 12, 14, 16, 18} or the SD of {100, 102, 104, 106, 108, 110, 112, 114, 116, 118}. That's because the second set is obtained by adding 2 to each term of the first set and the third set is obtained by adding 102 to each term of the first set.

20. Descriptive Statistics

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Hope it helps.
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Re: What is the variance of set X, which contains only consecutive even in &nbs [#permalink] 30 Apr 2018, 05:25
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