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# Which of the following triples of numbers have the same

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Which of the following triples of numbers have the same [#permalink]
zbvl wrote:
Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?

I. r-2, s-2, t-2
II. 0, r-s, t-s
III. r-4, s+5, t-1

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

SD is about finding the squareroot of the sum of difference of Avg of the numbers and the numbers individually. If we can find out the (Avg-Number) set same in given options then we can conclude that the SD is same.
In the above problem, the Avg of r,s,t is (r+s+t)/3 and the difference with each of the numbers are (s+t-2r)/3, (r+t-2s)/3 and (r+s-2t)/3. If you try to compute the difference in I & II sets, you will notice that the difference remains same for the sets.
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Re: Which of the following triples of numbers have the same [#permalink]
Her the rule is that the standard deviation does not change if we add or subtract same thing from all the numbers
Hence C
Also never ever make the mistake of choosing numbers here.
I used to do that ..
as some of them may satisfy the third case too..

Regards
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Re: Which of the following triples of numbers have the same [#permalink]
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?
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Re: Which of the following triples of numbers have the same [#permalink]
Keats wrote:
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?

Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.
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Re: Which of the following triples of numbers have the same [#permalink]
abhimahna wrote:
Keats wrote:
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?

Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.

Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below

a) s+1, t + 6, u +4
b) s+1, t+ 1, u+ 1

when you know s.d. of s,t,u is d, what will be your answer?
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Re: Which of the following triples of numbers have the same [#permalink]
Keats wrote:
abhimahna wrote:
Keats wrote:
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?

Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.

Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below

a) s+1, t + 6, u +4
b) s+1, t+ 1, u+ 1

when you know s.d. of s,t,u is d, what will be your answer?

HI THERE..!
The Thing is => The stem has asked that when will the SD remain the same. It impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U

Regards
Stone Cold
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Re: Which of the following triples of numbers have the same [#permalink]
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stonecold wrote:

HI THERE..!
The Thing is => The stem has asked that when will the SD remain the same. It impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U

Regards
Stone Cold

Thanks stonecold. As far as this question is concerned, I have no doubts. I just wanted to extend the learning and point that if we add/subtract same constant to r,s, and t there will be no change in the standard deviation and it will remain the same as that of r,s, and t.

However, if we add random constant to each r,s, and t then the standard deviation will definitely CHANGE. However, we will have to do calculation to it! So the case is that it should be the *same constant* that is added to r,s, and t.

I hope I am able to convey my point.
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Re: Which of the following triples of numbers have the same [#permalink]
Keats wrote:
abhimahna wrote:
Keats wrote:
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?

Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.

Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below

a) s+1, t + 6, u +4
b) s+1, t+ 1, u+ 1

when you know s.d. of s,t,u is d, what will be your answer?

For a, standard deviation will change since different constant is added to each term.
For b, standard deviation will not change since same constant is added to each term.
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Which of the following triples of numbers have the same [#permalink]
Keats wrote:
stonecold wrote:

HI THERE..!
The Thing is => The stem has asked that when will the SD remain the same. It impliesSITUATIONS WHEN SD WILL BE SAME IRRESPECTIVE OF THE VALUE OF S,T,U

Regards
Stone Cold

Thanks stonecold. As far as this question is concerned, I have no doubts. I just wanted to extend the learning and point that if we add/subtract same constant to r,s, and t there will be no change in the standard deviation and it will remain the same as that of r,s, and t.

However, if we add random constant to each r,s, and t then the standard deviation will definitely CHANGE. However, we will have to do calculation to it! So the case is that it should be the *same constant* that is added to r,s, and t.

I hope I am able to convey my point.

This Will clear Any Doubts you have Regarding Standard Deviation =>
math-standard-deviation-87905.html

Regards
Stone Cold
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Re: Which of the following triples of numbers have the same [#permalink]
Keats wrote:
abhimahna wrote:
Keats wrote:
Bunuel: Please confirm - When there is a different constant added to a list of numbers, does the standard deviation change?
For example: a, b, and c have s.d. 'x'
Will a+3, b+7, c+3 have s.d. 'x'?

Adding or subtracting doesn't change the standard deviation while multiplying or dividing does.

Looks like you have not read my question clearly. I understand adding/subtracting doesn't effect s.d. But if I ask you to calculate s.d. for below

a) s+1, t + 6, u +4
b) s+1, t+ 1, u+ 1

when you know s.d. of s,t,u is d, what will be your answer?

What I meant was adding or subtracting a constant term doesn't change the SD. Its like an AP, when you add or subtract a constant term to each o the term of an AP, it never changes.

Hence, in your options above, in a) you are adding a different rem to each of the terms, So SD will change

but in b) since you are adding a constant term to each of the terms, it would not have any impact.

I hope its clear now.
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Re: Which of the following triples of numbers have the same [#permalink]
Thanks abhimahna. Also thank you stonecold for sharing the standard deviation link. It is useful.
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Re: Which of the following triples of numbers have the same [#permalink]
In case of doubt, we can just put in a value and solve this question.
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Re: Which of the following triples of numbers have the same [#permalink]
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SD=difference of values from the mean(this is simplified definition but will serve the purpose)
Calculations are not required but we will do them to get the idea
Let r=10
s=15
t=20
mean=10+15+20/3=15
Difference of each value from mean
r
10-15=-5
s
15-15=0
t
20-15=5
let us look at answer choices
r-2=10-2=8
s-2=15-2=13
t-2=20-2=18
Average of new set=8+13+18/3=45/3=15
the difference from mean
r-2
8-13=-5
s-2
13-13=0
t-2
18-13=5
the difference is same as the 1st set and hence SD will be same.

2nd option
0
r-s=10-15=-5
t-s=20-15=5
this set contains 0,-5 and 5 same as 1st set.
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Re: Which of the following triples of numbers have the same [#permalink]
The rule is "the standard deviation of a set will not change If we add/ subtract a constant to each term in a set"
=> Sd of (r-2, s-2, t-2) = sd of (r,s,t) because set (r-2, s-2, t-2) obtained by subtract each term (r,s,t) by 2.
Sd of (0, r-s, t-s) = sd of (r,s,t) because set (o, r-s, t-s) obtained by subtract each term (r,s,t) by s.
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Re: Which of the following triples of numbers have the same [#permalink]
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zbvl wrote:
Which of the following triples of numbers have the same standard deviation as the numbers r, s, and t?

I. r-2, s-2, t-2
II. 0, r-s, t-s
III. r-4, s+5, t-1

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

We may recall the rule that when we add or subtract the same constant to a set of numbers the standard deviation does not change. Let’s analyze each Roman Numeral:

I. r-2, s-2, t-2

Since 2 is subtracted from r, s, and t, the standard deviation is the same as that of r, s, and t.

II. 0, r-s, t-s

If we subtract s from r, s, and t, we have r - s, s - s = 0, and t - s, thus the standard deviation is the same as that of r, s, and t.

III. r-4, s+5, t-1

We see that since we subtract/add different numbers to r, s, and t, we do not have the same standard deviation as that of r, s, and t.

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Re: Which of the following triples of numbers have the same [#permalink]
Hi Bunuel,
Is this question of Must be category or Could be category?
Its not explicitly mentioned in Question.
I am assuming it to be Must be Question. Is this understanding correct?
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Re: Which of the following triples of numbers have the same [#permalink]
We know, if same thing is added or subtracted to all the terms, standard deviation does not change.
I. r-2, s-2, t-2 (Subtracted 2 from each term) Same
II. 0, r-s, t-s (Subtracted s from each term) Same
III. r-4, s+5, t-1 (no common thing subtracted) Different

Hence, OA is (C).
Re: Which of the following triples of numbers have the same [#permalink]
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