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16 Nov 2010, 23:37
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I was using the Quant notes by "Target" and I came to this explanation:
Normal distribution follows the pattern: 2%, 14%, 34%, mean, 34%, 14%, 2%. Where to use:
Princeton Review Math Bin4, Q3. if question says mean of normal distribution is 72 and we can find
that 2% people are above 82. this means that 82 which is 2 standard deviations away (since 2% is
two steps away form mean,34% then 14%), thus one standard deviation is 82-72=10/2 = 5. Now
bottom 16% will be one standard deviation away from mean (left side, 2% +14%=16%) therefore, 72-
5=67.
I understand the basic principle of standard deviation, of how far numbers are from the mean, creating a bell curve distribution. However, to me this says if 72 is the mean and 1 standard deviation is 5, then 72(mean) 77(34) 82(14) 87(2%)... I know I am missing something so can someone please explain to me the distribution patter within this set of numbers? Thank you ahead of time.
Normal distribution follows the pattern: 2%, 14%, 34%, mean, 34%, 14%, 2%. Where to use:
Princeton Review Math Bin4, Q3. if question says mean of normal distribution is 72 and we can find
that 2% people are above 82. this means that 82 which is 2 standard deviations away (since 2% is
two steps away form mean,34% then 14%), thus one standard deviation is 82-72=10/2 = 5. Now
bottom 16% will be one standard deviation away from mean (left side, 2% +14%=16%) therefore, 72-
5=67.
I understand the basic principle of standard deviation, of how far numbers are from the mean, creating a bell curve distribution. However, to me this says if 72 is the mean and 1 standard deviation is 5, then 72(mean) 77(34) 82(14) 87(2%)... I know I am missing something so can someone please explain to me the distribution patter within this set of numbers? Thank you ahead of time.
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19 Nov 2010, 11:12
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mmcooley33
Let me start by saying that it is incredibly unlikely that you will EVER need to know this much detail about standard deviation on the GMAT. In my 20+ years of GMAT teaching experience, I have never seen nor heard of a real GMAT question that required you to know anything about a normal distribution.
That said, the concept with which your struggling is something that could come up in other contexts, so it's worth addressing the issue.
You've misinterpreted the original information slightly, which is why you're confused. Let's start with 1 SD from the mean.
In a normal distribution, 68% (34% + 34%) of data points are within 1 SD of the mean, "within" being the key word. So, in the example given, 68% of the numbers will be in the range 67 < x < 77.
Similarly, 68 + 28 = 96% of data points will be within 2 SDs of the mean. So, 96% of the numbers will be in the range 62 < x < 82.
We have 4% of the population remaining, so 2% will be less than 62 and 2% will be greater than 82.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
