Which of the following triples of numbers have the same

Question

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

Bunuel · Accepted Answer

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

Set {r-2, s-2, t-2} is obtained by subtracting 2 from each term of {r, s, t}.
Set {0, r-s, t-s} is obtained by subtracting s from each term of {r, s, t}.
Set {r-4, s+5, t-1} is totally different from {r, s, t}.

Thus the answer is I and II only.

Answer: C.

Bunuel · Answer

Similar questions to practice. PS: if-d-is-the-standard-deviation-x-y-and-z-what-is-the-stan-93979.html m11-72303.html m05-71689.html#p1145328 m03-72087.html which-of-the-following-sets-has-the-standard-deviation-131485.html set-a-consists-of-all-even-integers-between-2-and-110876.html set-a-consists-of-all-prime-numbers-between-10-and-25-set-b-110874.html a-certain-list-of-100-data-has-an-average-arithmetic-mean-87743.html DS: let-s-be-a-finite-set-of-consecutive-multiples-of-155075.html if-q-is-a-set-of-consecutive-integers-what-is-the-standard-151794.html is-the-standard-deviation-of-the-numbers-x-y-and-z-equal-to-145906.html a-researcher-computed-the-mean-the-median-and-the-standard-134893.html during-an-experiment-some-water-was-removed-from-each-of-94166.html what-is-sd-of-given-set-of-numbers-whose-average-is-104000.html there-is-a-set-of-consecutive-even-integers-what-is-the-98877.html Hope this helps.

Amit0507 · Answer

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.

stonecold · Answer

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

keats · Answer

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'?

abhimahna · Answer

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

keats · Answer

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?

stonecold · Answer

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

Regards
Stone Cold

keats · Answer

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.

Donnie84 · 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.

stonecold · Answer

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

abhimahna · 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.

gps5441 · Answer

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.
hence answer is C.

anhht13 · Answer

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.
Hence, the answer is C.

JeffTargetTestPrep · Answer

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.

Answer: C

v12345 · Answer

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).

harryzhang · Answer

got wrong bc i did not fully understand the formula and properties of standard deviation, so here's my lengthy note to self and hopefully help someone else

believe understanding standard deviation (and also variance) is the key to never get these types of questions wrong again, so let's dig in

definition: standard deviation is the square root of the variance, which equals the average squared difference from the mean
 
let's use the data set: 2, 4, 6, 8, 10 for instance

step 1: calculate the mean
 mean = 6

step 2: calculate the sum of squared difference for each term (i.e., each term subtract mean and then squared)
 (2-6)^2 = 16
(4-6)^2 = 4
(6-6)^2 = 0
(8-6)^2 = 4
(10-6)^2 = 16
sum = 40

step 3: calculate variance
 variance = avg. of squared difference for each term = 40/5 = 8

step 4: calculate standard deviation
 standard deviation = squared root of variance = root 8, or ~2.83

awesome, now let's explore the properties more.

what if we add 2 to each term?
data set is now: 4, 6, 8, 10, 12

repeating the process, we see:
mean = 8
sum = 40
variance = 40/5 = 8
standard deviation = root 8, or ~2.83
*note that since sum of squared difference still equals 40 here, variance and standard deviation will certainly be the same

what if we subtract 2?
data set is now: 0, 2, 4, 6, 8

same thing, we see:
mean = 4
sum = 40
variance = 40/5 = 8
standard deviation = root 8, or ~2.83
*same as above

here, we discovered that if we add or subtract a constant to each term in this set, the standard deviation will not change
  
applying the properties to question below

set {r-2, s-2, t-2} is obtained by subtracting 2 from each term of {r, s, t} -> good

set {0, r-s, t-s} is obtained by subtracting s from each term of {r, s, t} -> good

set {r-4, s+5, t-1} is obtained by adding random constants and thus def shift standard deviation -> bad

thus (C) I and II only

the legend  Bunuel  also posted other similar questions for practice, posting here as note to self; hope everyone here never make these mistakes again!

PS: 
 if-d-is-the-standard-deviation-x-y-and-z-what-is-the-stan-93979.html 
 m11-72303.html 
 m05-71689.html#p1145328 
 m03-72087.html 
 which-of-the-following-sets-has-the-standard-deviation-131485.html 
 set-a-consists-of-all-even-integers-between-2-and-110876.html 
 set-a-consists-of-all-prime-numbers-between-10-and-25-set-b-110874.html 
 a-certain-list-of-100-data-has-an-average-arithmetic-mean-87743.html

DS: 
 let-s-be-a-finite-set-of-consecutive-multiples-of-155075.html 
 if-q-is-a-set-of-consecutive-integers-what-is-the-standard-151794.html 
 is-the-standard-deviation-of-the-numbers-x-y-and-z-equal-to-145906.html 
 a-researcher-computed-the-mean-the-median-and-the-standard-134893.html 
 during-an-experiment-some-water-was-removed-from-each-of-94166.html 
 what-is-sd-of-given-set-of-numbers-whose-average-is-104000.html 
 there-is-a-set-of-consecutive-even-integers-what-is-the-98877.html

Which of the following triples of numbers have the same

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following triples of numbers have the same

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards