## The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the

##### This topic has expert replies
Moderator
Posts: 2053
Joined: 29 Oct 2017
Followed by:2 members

### The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the

by AAPL » Tue Nov 02, 2021 11:51 am

00:00

A

B

C

D

E

## Global Stats

Princeton Review

The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50

OA B

### GMAT/MBA Expert

GMAT Instructor
Posts: 16066
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

### Re: The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains

by [email protected] » Wed Nov 03, 2021 7:11 am
AAPL wrote:
Tue Nov 02, 2021 11:51 am
Princeton Review

The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50

OA B
-----------ASIDE-----------------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
----------------------------------

The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

2 standard deviations ABOVE the mean = 46 + 2(4) = 54
2 standard deviations BELOW the mean = 46 - 2(4) = 38

The range = 38 to 54

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

### GMAT/MBA Expert

GMAT Instructor
Posts: 6453
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:26 members

### Re: The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains

by [email protected] » Fri Nov 05, 2021 7:35 am
AAPL wrote:
Tue Nov 02, 2021 11:51 am
Princeton Review

The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

A. 38 to 46
B. 38 to 54
C. 42 to 50
D. 44 to 48
E. 46 to 50

OA B
Two standard deviations above the mean is 46 + 2(4) = 46 + 8 = 54.

Two standard deviations below the mean is 46 - 2(4) = 46 - 8 = 38.