A data set with a mean of 60 has a standard deviation of 3.5

Question

A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53 
B. 56 
C. 59 
D. 63.5 
E. 65

Bunuel · Accepted Answer

One standard deviation of the mean is from {mean}-{deviation}=60-3.5=56.5 to {mean}+{deviation}=60+3.5=63.5 . The smallest number within this range from the options is 59. Answer: C. Hope it's clear. Similar questions to practice: arithmetic-mean-and-standard-deviation-of-a-certain-normal-104117.html 70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html a-certain-characteristic-in-a-large-population-has-a-143982.html a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html the-residents-of-town-x-participated-in-a-survey-83362.html the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html the-mean-and-the-standard-deviation-of-the-8-numbers-shown-98248.html the-lifetime-of-all-the-batteries-produced-by-a-certain-comp-101472.html the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html a-certain-set-of-numbers-has-an-average-arithmetic-mean-of-161986.html Hope this helps.

BrentGMATPrepNow · Answer

-----------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    9  + 2(4) =  17 ]  
1.5 standard deviations BELOW the mean =  3    9  - 1.5(4) =  3 ]  
3 standard deviations ABOVE the mean =  21    9  + 3(4) =  21 ]  
etc.
-----------ONTO THE QUESTION-----------------------

A data set with a mean of  60  has a standard deviation of 3.5.   
So, 1 standard deviation ABOVE the mean =  60  + 3.5 = 63.5
And 1 standard deviation BELOW the mean =  60  - 3.5 = 56.5

Which of the following is the smallest number that falls within one standard deviation of the mean?   
The values within one standard deviation of the mean are all values that are  greater than or equal to 56.5  AND  less than or equal to 63.5 
So, when we check the answer choices, we see that   59   is the smallest value that fits with the above range of values.

Answer: C

Cheers,
Brent

kinjiGC · Answer

I guess the question is little ambiguous. I didn't understand what "one standard deviation" meant. I took at as a number.
As  ^1/2 = 1
So 59 satisfies that criteria.

gmatbugsme84 · Answer

56 is smaller than 56.5 and does not lie in between 56.5 and 63.5 (the specified range here). I think you meant 59. Answer C. No?

Bunuel · Answer

Yes. Edited the typo. Thank you.

CrackverbalGMAT · Answer

One standard deviation of the mean = 60 - 3.5 = 56.5 OR 60 + 3.5 = 63.5

From the answer options only 59 falls in this criteria hence answer is C.

Abhishek009 · Answer

Range is =  Mean   +   SD

Range = 60   +   3.5

Ie, Range is 56.5 to 63.5
 
Thus, among the given options only (C) 59 falls within the given range, answer will be (C)

JeffTargetTestPrep · Answer

Since one standard deviation below the mean is 60 - 3.5 = 56.5, 53 and 56 will fall outside one standard deviation of the mean. So 59 is the smallest number in the given answer choices that falls within one standard deviation of the mean.

Alternate Solution:

One standard deviation below the mean is 60 - 3.5 = 56.5, and one standard deviation above the mean is 60 + 3.5 = 63.5. Thus, we are looking for the smallest data value that falls in the interval from 56.5 to 63.5. We see from the answer choices that 59 meets the requirement.

Answer: C

MathRevolution · Answer

A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

Mean = 60 and S.D. = 3.5

Numbers within one standard deviation of the mean:

Mean + S.D. = 60 + 3.5 = 63.5
Mean - S.D. = 60 - 3.5 = 56.5

The smallest number within this interval of 56.5 to 63.5 is 59.

Answer C

bumpbot · Answer

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A data set with a mean of 60 has a standard deviation of 3.5

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