An issue regarding a standard deviation calculation

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lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 amFollowed by: 1 member

by lukaswelker » Tue Apr 01, 2014 1:03 am

Hey guys here is the question

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television per week.
30;20;18;12;6

Following my calculations the answer should be 18, but at the end it’s 12. What am I doing wrong?

Source: Beat The GMAT — Problem Solving | Tue Apr 01, 2014 1:03 am

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by GMATGuruNY » Tue Apr 01, 2014 2:15 am

Residents of Town X participated in a survey to determine the no. of hrs per week each resident spent watching TV.The distribution of results of the survey had a mean of 21 hrs an a standard dev of 6 hrs. The no. of hrs that Pat, a resident of Town X, watched TV, last week was between 1 and 2 standard dev below mean. Which of the following could be the number of hrs that Pat watched TV last week?

A. 30
B. 20
C.18
D.12
E. 6

Let SD = standard deviation.

Given information:
Mean = 21.
SD = 6.

One SD below the mean = 21-6 = 15.
Two SD's below the mean = 15-6 = 9.
Thus, the number of hours watched must be between 9 and 15.

The correct answer is D.

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by Brent@GMATPrepNow » Tue Apr 01, 2014 7:22 am

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.

Here's a video that covers the necessary concepts/skills to answer this question: https://www.gmatprepnow.com/module/gmat ... /video/809

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