The table above shows the GPA of 20 students last semester.

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Jan 28, 2019 7:43 am

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The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?

A. None
B. 1
C. 2
D. 3
E. 4

The OA is E

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Mon Jan 28, 2019 7:43 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 28, 2019 8:34 am

swerve wrote:

The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?

A. None
B. 1
C. 2
D. 3
E. 4

---------------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.
----ONTO THE QUESTION!!!------------------------

The average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6
1.5 standard deviations ABOVE the mean = 2.95 + 1.5(0.6) = 3.85
1.5 standard deviations BELOW the mean = 2.95 - 1.5(0.6) = 2.05

How many of the grades are MORE THAN 1.5 standard deviations away from the mean?
So, we're looking for grades that are EITHER less than 2.05 OR greater than 3.85

Check the values....

There are 4 such values.

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Jan 28, 2019 9:31 am

swerve wrote:

The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?

A. None
B. 1
C. 2
D. 3
E. 4
Source: Veritas Prep

$$\left( {\mu \,;\,\sigma } \right) = \left( {2.95\,;\,0.6} \right)$$
$$?\,\,\,:\,\,\,\left| {{\text{grade}} - \mu } \right| > 1.5\sigma \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\text{grade}}\,\, < \,\,\mu - 1.5\sigma \,\, = \,\,2.05\,\,\,\,\underline {{\text{or}}} \,\,\,\,{\text{grade}} > \mu + 1.5\sigma = 3.85$$
$${\text{?}}\,\,{\text{ = }}\,\,4\,\,{\text{cases}}\,\,\,\left( {{\text{by}}\,\,{\text{inspection}}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jan 30, 2019 6:01 pm

swerve wrote:

The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?

A. None
B. 1
C. 2
D. 3
E. 4

The OA is E

Source: Veritas Prep

1.5 standard deviations is 1.5 x 0.6 = 0.9.

So 1.5 standard deviations above the mean is 2.95 + 0.9 = 3.85, and 1.5 standard deviations below the mean is 2.95 - 0.9 = 2.05.

Looking at the chart, we see that 4 grades (1.8, 4.0, 1.9 and 3.9) are more than 1.5 standard deviations away from the mean.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
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