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DS Q There is set of consecutive even integers. What is S.D? 31 Jan 2012, 02:28
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There is a set of consecutive even integers. What is the Standard deviation of the set ?
1)There are 39 elements in the set.
2)The mean of the set is 382.

The answer to this question is A. Can someone explain the logic behind this ?
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DS Q There is set of consecutive even integers. What is S.D? 31 Jan 2012, 03:10
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Hi

In order to solve this problem we need to know the mean & the terms of the sample.

Statement A :
Gives us 39 consecutive even elements
Eg : 0,2,4,.....
To Compute SD
1. Compute the difference of each data point from the mean, and square the result of each
2. compute the average of these values, and take the square root

Which we can calculate easily from the given data

Thus statement A is sufficient

Statement B
Mean is 382 only gives us the mid point of the set but not the number of elements hence we cannot calculate the SD

Thus statement B is insufficient

Hope this helps
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DS Q There is set of consecutive even integers. What is S.D? 31 Jan 2012, 08:19
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Thanks man
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DS Q There is set of consecutive even integers. What is S.D? 09 Apr 2016, 00:20
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boomtangboy
Hi

In order to solve this problem we need to know the mean & the terms of the sample.

Statement A :
Gives us 39 consecutive even elements
Eg : 0,2,4,.....
To Compute SD
1. Compute the difference of each data point from the mean, and square the result of each
2. compute the average of these values, and take the square root

Which we can calculate easily from the given data

Thus statement A is sufficient

Statement B
Mean is 382 only gives us the mid point of the set but not the number of elements hence we cannot calculate the SD

Thus statement B is insufficient

Hope this helps
Show more

Dear Experts,

Please explain how statement A is sufficient to calculate standard deviation.

From the given information which 39 even elements we need to consider .

IMO these 39 elements can be from 0,2,4.... or from 100,102,104...

will the standard deviation calculated from any of the 'n' number of even integers is same?

Please advise
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DS Q There is set of consecutive even integers. What is S.D? 09 Apr 2016, 00:37
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smartguy595
boomtangboy
Hi

In order to solve this problem we need to know the mean & the terms of the sample.

Statement A :
Gives us 39 consecutive even elements
Eg : 0,2,4,.....
To Compute SD
1. Compute the difference of each data point from the mean, and square the result of each
2. compute the average of these values, and take the square root

Which we can calculate easily from the given data

Thus statement A is sufficient

Statement B
Mean is 382 only gives us the mid point of the set but not the number of elements hence we cannot calculate the SD

Thus statement B is insufficient

Hope this helps

Dear Experts,

Please explain how statement A is sufficient to calculate standard deviation.

From the given information which 39 even elements we need to consider .

IMO these 39 elements can be from 0,2,4.... or from 100,102,104...

will the standard deviation calculated from any of the 'n' number of even integers is same?

Please advise
Show more

hi,
since the elments are consecutive and number of elements are same, SD will remain same..

For SD we take out AVERAGE and subtract each number from it...
two cases
1) 0,2,4....38*2
average = 19*2 = 38..
subtract ecah number 38-0 = 38 and 38-2 = 36 and so on
2) 100,102.... 100+38*2
average = 100+19*2 = 138
Difference 138-100=38 and 136-2 = 36..

so you see the difference is the same..
SD depend s on HOW far the numbers are SPREAD..
and in each case with 39 consecutive elements, the numbers are equally spread
Hope it helps
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DS Q There is set of consecutive even integers. What is S.D? 09 Apr 2016, 07:01
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chetan2u
smartguy595
boomtangboy
Hi

In order to solve this problem we need to know the mean & the terms of the sample.

Statement A :
Gives us 39 consecutive even elements
Eg : 0,2,4,.....
To Compute SD
1. Compute the difference of each data point from the mean, and square the result of each
2. compute the average of these values, and take the square root

Which we can calculate easily from the given data

Thus statement A is sufficient

Statement B
Mean is 382 only gives us the mid point of the set but not the number of elements hence we cannot calculate the SD

Thus statement B is insufficient

Hope this helps

Dear Experts,

Please explain how statement A is sufficient to calculate standard deviation.

From the given information which 39 even elements we need to consider .

IMO these 39 elements can be from 0,2,4.... or from 100,102,104...

will the standard deviation calculated from any of the 'n' number of even integers is same?

Please advise

hi,
since the elments are consecutive and number of elements are same, SD will remain same..

For SD we take out AVERAGE and subtract each number from it...
two cases
1) 0,2,4....38*2
average = 19*2 = 38..
subtract ecah number 38-0 = 38 and 38-2 = 36 and so on
2) 100,102.... 100+38*2
average = 100+19*2 = 138
Difference 138-100=38 and 136-2 = 36..

so you see the difference is the same..
SD depend s on HOW far the numbers are SPREAD..
and in each case with 39 consecutive elements, the numbers are equally spread
Hope it helps
Show more
Thanks for the explanation chetan2u
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DS Q There is set of consecutive even integers. What is S.D? 23 Apr 2021, 14:13
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Most of the people are confusion because it specifies the number of elements but doesn't specify actual numbers, but remember it can still be calculated, see below:
Assume even numbers to be: 0, 2, 4 .....

Then remember the property of SD? Decrease/increase in all elements of a set by a constant value DOES NOT decrease/increase standard deviation of the set. This property, if you remember, is helpful in thinking ahead and getting correct answer.