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11 May 2015, 11:37
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E
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In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?
a) 48
b) 60
c) 72
d) 77.5
e) 81
a) 48
b) 60
c) 72
d) 77.5
e) 81
11 May 2015, 18:30
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Hi zxcvbnmas,
Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 60
2) The standard deviation of the group is 12
If you go 1 SD "up" from the average, you hit.....60+12 = 72
If you go 1 SD "down" from the average, you hit.....60-12 = 48
If you go 2 SDs "up" from the average, you hit.....60+2(12) = 84
If you go 2 SDs "down" from the average, you hit.....60-2(12) = 36
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDs "up" would be.....60 + 1.75(12) = 81
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 60
2) The standard deviation of the group is 12
If you go 1 SD "up" from the average, you hit.....60+12 = 72
If you go 1 SD "down" from the average, you hit.....60-12 = 48
If you go 2 SDs "up" from the average, you hit.....60+2(12) = 84
If you go 2 SDs "down" from the average, you hit.....60-2(12) = 36
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDs "up" would be.....60 + 1.75(12) = 81
Final Answer:
GMAT assassins aren't born, they're made,
Rich
20 Apr 2018, 14:52
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zxcvbnmas
--------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.
----NOW ONTO THE QUESTION!!!!-----------------------------
1.75 standard deviations more than (aka ABOVE) the mean = 60 + (1.75)(12)
= 60 + 21
= 81
= E
Cheers,
Brent
