Last visit was: 23 Jul 2024, 20:09 It is currently 23 Jul 2024, 20:09
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If d is the standard deviation x, y, and z, what is the standard devia

SORT BY:
Tags:
Show Tags
Hide Tags
Senior Manager
Joined: 03 Sep 2006
Posts: 445
Own Kudos [?]: 6905 [63]
Given Kudos: 33
Math Expert
Joined: 02 Sep 2009
Posts: 94589
Own Kudos [?]: 643392 [101]
Given Kudos: 86728
Manager
Joined: 04 May 2010
Posts: 61
Own Kudos [?]: 335 [7]
Given Kudos: 7
Q51  V44
GPA: 3.8
WE 1: 2 yrs - Oilfield Service
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30854 [2]
Given Kudos: 799
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
1
Kudos
1
Bookmarks
Top Contributor
LM wrote:
If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ?

A. d
B. 3d
C. 15d
D. d + 5
E. d + 15
Attachment:
PS8.PNG

Adding the same value to each value in a set does not change the standard deviation of the set.

So, the standard deviation of {x + 5, y + 5, z + 5 } will also be d.

General Discussion
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6027
Own Kudos [?]: 13822 [6]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
4
Kudos
2
Bookmarks
LM wrote:
If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ?

A. d
B. 3d
C. 15d
D. d + 5
E. d + 15

CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.

1) It depends on the separation between the successive terms of the set

2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}

3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}

When 5 is added in each term of set {x, y, z} then the new set {x+5, y+5, z+5} will remain same as the previous standard deviation i.e. d

Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19189
Own Kudos [?]: 22704 [2]
Given Kudos: 286
Location: United States (CA)
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
2
Kudos
LM wrote:
If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ?

A. d
B. 3d
C. 15d
D. d + 5
E. d + 15

In a data set, if every number is increased (or decreased) by the same amount, the standard deviation of the data set will not be affected. That is, the new standard deviation is still equal to the original standard deviation. Here we see that each data value is increased by the same amount (5 in this case); therefore, the standard deviation will still be d.

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11795 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
3
Kudos
Hi All,

In real basic terms, Standard Deviation is a measure of how "spread out" a group of numbers is. Numbers that are "close together" will create a small Standard Deviation, while numbers that are really "spread out" will create a large Standard Deviation.

Here, we have 3 values: X, Y and Z. We're told that they have a Standard Deviation of D.

X = 1
Y = 2
Z = 3
Standard Deviation = D (don't worry about calculating it, the GMAT will NEVER ask you to calculate a Standard Deviation)

Notice the "spread" of the above numbers; we'll come back to this in a moment.

The question then asks us to think about X+5, Y+5 and Z+5. Using the values from above, we would have….
1+5 = 6
2+5 = 7
3+5 = 8

Now, notice how these values have the exact SAME SPREAD as the initial set of numbers? This group of numbers has the SAME STANDARD DEVIATION as the original set of numbers. Thus, the Stand Deviation is still D.

GMAT assassins aren't born, they're made,
Rich
Intern
Joined: 30 Sep 2021
Posts: 15
Own Kudos [?]: 13 [0]
Given Kudos: 1
If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
LM wrote:
If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ?

A. d
B. 3d
C. 15d
D. d + 5
E. d + 15

Attachment:
PS8.PNG

Similar to this one,
If x is the standard deviation of a, b, c, d, e, and y is the standard deviation of a-3, b-2, c, d+2, e+3.
which one is greater? Bunuel sir

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11795 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
2
Kudos
1
Bookmarks
COolguy101 wrote:
LM wrote:
If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ?

A. d
B. 3d
C. 15d
D. d + 5
E. d + 15

Attachment:
PS8.PNG

Similar to this one,
If x is the standard deviation of a, b, c, d, e, and y is the standard deviation of a-3, b-2, c, d+2, e+3.
which one is greater? Bunuel sir

Hi COolguy101,

The answer to your question will depend on the relative values of A, B, C, D and E (since increasing/decreasing a value can have a distinct effect on the S.D. of the entire group).

For example:

IF.... A = B = C = D = E = 3, then...
the first group is {3, 3, 3, 3, 3}
the second group is {0, 1, 3, 5, 6}

Here, the the S.D. of the first group would be 0 (since all 5 values are the same) and the S.D. of the second group would be larger.

However,

IF.... A = 3, B = 2, C = 0, D = -2, E = -3, then....
the first group is {3, 2, 0, -2, -3}
the second group is {0, 0, 0, 0, 0}

Here, the the S.D. of the second group would be 0 (since all 5 values are the same) and the S.D. of the first group would be larger.

GMAT assassins aren't born, they're made,
Rich
Non-Human User
Joined: 09 Sep 2013
Posts: 34052
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If d is the standard deviation x, y, and z, what is the standard devia [#permalink]
Moderator:
Math Expert
94589 posts