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#1
04-30-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534
Normal Gaussian Distribution

Please someone explain me this, i know it should be easier but when it comes to math i tend to forget things, on DIT there's a Question like this...

"" Assuming a normal Gaussian distribution for the results of a particular test and a mean value of 35 and
SD of 4, what percentage of people will be in the interval between 31 and 43? """

Please explain me the approach so I can understand further question regarding this matter...
 The above post was thanked by: struggle (05-27-2011)

#2
04-30-2011
 Ex-USMLE Forums Staff Steps History: 1+CK+CS+3 Posts: 753 Threads: 106 Thanked 2,196 Times in 465 Posts Reputation: 2244

You can see in the normal distribution curve that 68.2% of records within +/- one standard deviation and 95.4% within +/- two standard deviations and 34.1% of records are between the mean and +1SD and 13.6% records between +1SD to +2SD ...etc

the middle value is 35 and the SD is 4
Mean - 1SD = 35-4 = 31
Mean + 1SD = 35+4 = 39
Mean + 2SD = 35+8 = 43

So now you have to see (using the curve above) what percentage of values fall between 31 and 43

Can you get the answer now?
 The above post was thanked by: aknz (10-08-2011), asfand (05-01-2011), doc_study (04-30-2011), INCOGNITO (03-05-2012), kiki (05-31-2011), madeha shahid (03-06-2012), Mondoshawan (04-30-2011), prataptetali (04-30-2011), rulz (04-30-2011), struggle (05-27-2011)
#3
04-30-2011
 USMLE Forums Master Steps History: 1+CK+CS Posts: 590 Threads: 31 Thanked 1,232 Times in 411 Posts Reputation: 1256

You need to know that, in a normal curve, ~68% of the area is contained within one standard deviation of the mean, ~95% within two standard deviations, and ~99% within three standard deviations. So the answer to your question would be 68%. Remember that there are two tails to the curve, so they could ask something confusing like "what percent falls below 43 (for your example)", and you would have to include 68% plus 1/2 of 32% (= 16%, i.e. the lower tail), for a total of 84%.

edit: haha! I see that Lee has faster fingers than I do!
 The above post was thanked by: asfand (05-01-2011), ibukun (05-26-2011), lee-usmle (04-30-2011), madeha shahid (03-06-2012), rulz (04-30-2011), struggle (05-27-2011), zitney (04-30-2011)

#4
04-30-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Hey Lee-usmle,

I think i got it... But another question how do you come up with the numbers of 34.1 13.6 and 2.15 ? That's the same exact approach that brian jekins on DIT did...

Im really grateful ... Thanks!!!
#5
04-30-2011
 Ex-USMLE Forums Staff Steps History: 1+CK+CS+3 Posts: 753 Threads: 106 Thanked 2,196 Times in 465 Posts Reputation: 2244

Quote:
 Originally Posted by rulz Hey Lee-usmle, I think i got it... But another question how do you come up with the numbers of 34.1 13.6 and 2.15 ? That's the same exact approach that brian jekins on DIT did... Im really grateful ... Thanks!!!
These are standard numbers in the normal distribution curve. These numbers are by definition and by consensus, they did not come from calculation or whatever.
My advice, you should memorize these numbers
 The above post was thanked by: madeha shahid (03-06-2012), rulz (04-30-2011), struggle (05-27-2011), zitney (04-30-2011)
#6
04-30-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Quote:
 Originally Posted by lee-usmle These are standard numbers in the normal distribution curve. These numbers are by definition and by consensus, they did not come from calculation or whatever. My advice, you should memorize these numbers
Thanks sir, you helpd me with that ... Now i understand, My lowers score are Behaivoral , Molecular biology and Genetics... so im trying to understand every little steps on those...

USMLE-FoRums! Rocks!...

Thanks again i write it down on my book... =)
#7
04-30-2011
 USMLE Forums Scout Steps History: Not yet Posts: 46 Threads: 3 Thanked 34 Times in 20 Posts Reputation: 44

Quote:
 Originally Posted by lee-usmle These are standard numbers in the normal distribution curve. These numbers are by definition and by consensus, they did not come from calculation or whatever. My advice, you should memorize these numbers
Well they did come from calculations I think (area under the curve etc.) but yes definitely memorise these numbers.
#8
04-30-2011
 USMLE Forums Addict Steps History: 1+CK+CS Posts: 144 Threads: 47 Thanked 41 Times in 28 Posts Reputation: 51

Quote:
 Originally Posted by lee-usmle You can see in the normal distribution curve that 68.2% of records within +/- one standard deviation and 95.4% within +/- two standard deviations and 34.1% of records are between the mean and +1SD and 13.6% records between +1SD to +2SD ...etc In your example. the middle value is 35 and the SD is 4 Mean - 1SD = 35-4 = 31 Mean + 1SD = 35+4 = 39 Mean + 2SD = 35+8 = 43 So now you have to see (using the curve above) what percentage of values fall between 31 and 43 Can you get the answer now?
sry but i couldnt understand why we add 8 for 2 sd deviation and what percentage we calculate like this even iam weak in such things any advice
#9
05-01-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Quote:
 Originally Posted by priya1 sry but i couldnt understand why we add 8 for 2 sd deviation and what percentage we calculate like this even iam weak in such things any advice
Hy priya,

Look over the question, and it says that they used a SD of 4 and the mean being 35... So it means that all the inverval you are going to do are 4 point apart...
ex.------- etc - 27 - 31 - 35 - 39 - 43 - etc -------

Then the real question is asking you which porcent will be at 31 ( 1 SD ) and which at 43 ( 2 SD )

If you check the table now... you will understand that... When you go down to 31... just 1... then when going up 35 - 39 - 43 ... you go up 2SD.

when you go 1 SD the percentage are 68.2 , 2 SD 95.4 and 3SD 99.7 <-- which those are "constant" number over the standard deviation.

Now re-read this and go over the LEE-USMLE graphic and you will understand better....
 The above post was thanked by: asfand (05-01-2011), struggle (05-27-2011)
#10
05-01-2011
 USMLE Forums Addict Steps History: 1+CK+CS Posts: 144 Threads: 47 Thanked 41 Times in 28 Posts Reputation: 51

Quote:
 Originally Posted by rulz Hy priya,.......
thanks now i can understand
#11
05-01-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Always a pleasure prya! remember ppl to take at least 1 day off when you are fully studying.... so brain can rest =)
#12
05-26-2011
 USMLE Forums Guru Steps History: Not yet Posts: 324 Threads: 70 Thanked 238 Times in 144 Posts Reputation: 248

Actually i have a confusion over some point..as if in a sample of 500 apparently healthy individuals the blood glucose level seem to be distributed with the mean of 90 mg/dl and a SD of 5mg/dl,what % of students will has blood glucose values in the shaded area(that is area shaded from +95 and above)
Uworld explain it like this that 68% of students fall within 1SD (btwn 85 and 95)the rest of the student (that is the shaded area) will be 100% -68%=32%
32%/2=16% (will fall in the shaded area)
I tried to solve the question posted above by RULZ by following the same strategy but i gt 84% as an answer..AM i right?
CAN I SOLVE THE QUESTION LIKE THIS?
#13
05-26-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Quote:
 Originally Posted by struggle Actually i have a confusion over some point..as if in a sample of 500 apparently healthy individuals the blood glucose level seem to be distributed with the mean of 90 mg/dl and a SD of 5mg/dl,what % of students will has blood glucose values in the shaded area(that is area shaded from +95 and above) Uworld explain it like this that 68% of students fall within 1SD (btwn 85 and 95)the rest of the student (that is the shaded area) will be 100% -68%=32% 32%/2=16% (will fall in the shaded area) I tried to solve the question posted above by RULZ by following the same strategy but i gt 84% as an answer..AM i right? CAN I SOLVE THE QUESTION LIKE THIS? PLZ REPLY

Yes, I did the your problem,

i resolve it like this, I took the Mean which is 90 and SD of 5,,, so The question as i understand is asking you... who are the ppl who will be at 95 mg/dl ... which have to make you believe that is 1 SD of the mean,, so according the values that the question gave u... 85 - 90 - 95 ...

So you can see that 1 SD of the mean means 68. So is like this, 100 - 68 = 32 on BOTH SIDE
To get to each side just do 32/2 = 16.

so now, in one side you will have 16%... for the 95 mg/dl.

... For better understanding Try to do it over a Graph ...

so you dont have to do any futher calculation, check it...

Attached Thumbnails

Last edited by rulz; 05-26-2011 at 09:25 AM.
 The above post was thanked by: bebix (05-26-2011), struggle (05-27-2011)
#14
05-26-2011
 USMLE Forums Scout Steps History: Not yet Posts: 20 Threads: 0 Thanked 15 Times in 14 Posts Reputation: 25

i think this can be understood in practical sense A normal curve just shows the distribution of variables about the mean value i.e how close or far a value is from the mean It might be less than or greater than the mean It also gives the proportion i.e percentage of variables less than i.e to the left of the mean and greater than to the right of the mean The whole curve is 100% ,50% are less than the mean and 50% are greater So if a mean of 90 is given and SD of 5 ,95 is 95-90/5 SD from the mean i.e 1 SD from the mean and it is greater than the mean It also falls within the 68% i.e 68% evenly distributed around the mean with half (34%) on each side. % greater than 95 will be what is left on the right side i.e side greater than the mean i.e 50-34 =16 i think u can use this with the other explanations and graphs Hope it is not too long and boring
 The above post was thanked by: struggle (05-27-2011)
#15
05-27-2011
 USMLE Forums Guru Steps History: Not yet Posts: 324 Threads: 70 Thanked 238 Times in 144 Posts Reputation: 248

thanks ..yes i got ur point.But my question is this if i have to calculate the no. of students falling btwn 31 and 43 with a mean of 35 and SD of 4 (AS IN RULZ'S QUESTION) then wouldnt it be equal to 81%?becoz 68% of people fall between 31 and 39 and 95 within 2SD above or below the mean so we will add 68%+13.2%=81%
I dont know which point i am missing.

#16
05-27-2011
 USMLE Forums Addict Steps History: 1 + CS Posts: 113 Threads: 8 Thanked 89 Times in 61 Posts Reputation: 99

Quote:
 Originally Posted by struggle thanks ..yes i got ur point.But my question is this if i have to calculate the no. of students falling btwn 31 and 43 with a mean of 35 and SD of 4 (AS IN RULZ'S QUESTION) then wouldnt it be equal to 81%?becoz 68% of people fall between 31 and 39 and 95 within 2SD above or below the mean so we will add 68%+13.2%=81% I dont know which point i am missing.
You're right:

So, the mean value is 35 and one SD = 4

then, from 31 to 43 you will have:
95.4 - 13.6 = 81.8% or 68.2 + 13.6 = 81.8%
 The above post was thanked by: bebix (05-27-2011), rulz (05-27-2011), struggle (05-27-2011)
#17
05-27-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

Yes, that's right, 81% its falling into that range. At first, i though you were asking your case, not mine. Now you have
both cases.

If you look at the picture, you will see that

31 - 35 - 39 = 68 % which is 1 SD.

But the Question is asking, What would be from 1 SD to the LEFT ( 31 - 35 ) and 2 SD to the RIGTH ( 35 - 39 - 43 )

So, make it simple, 31 - 35 -39 = 68.2 % ( both side of the curve 34.1 + 34.1 )

and now just looking the other SD to the right 39 - 43 ( just 13.6 )

Plotting the numbers 68.2 + 13.6 = 81.8 % is the answer.

Last edited by rulz; 05-27-2011 at 07:09 AM.
 The above post was thanked by: struggle (05-27-2011)
#18
05-27-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 567 Threads: 25 Thanked 524 Times in 263 Posts Reputation: 534

If the question ask for both side ( 2 SD in both Side 27 - 31- 35 - 39 - 43 ) then in that case it would be 95.4 %...

Hope it helps...

I think now you can understand clearly the tricky of the question.
 The above post was thanked by: Claus_CU (05-27-2011), struggle (05-27-2011)
#19
03-05-2012
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 653 Threads: 47 Thanked 409 Times in 249 Posts Reputation: 419

Quote:
 Originally Posted by AbSa a question says tht a student scores 45 % in a test , mean 30% and SD 5% and in another test scores 60% , mean 40 % and SD 10 % ..in which test does he scores better, can anyone please explain thank you
In the first exam, he scores 3SD above the mean, meaning he is above 99% of test takers. (top 1 %)

In the second exam he scored 2 SD above the mean, meaning he is only above 97.5% of the test takers. (top 2.5%)

My answer would be, he did better in the first exam.
 The above post was thanked by:
#20
03-05-2012
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 653 Threads: 47 Thanked 409 Times in 249 Posts Reputation: 419

Quote:
 Originally Posted by AbSa how did you make out first one is 3SD and second one 2SD ..thanks

For the first one:

Mean was 30, SD was 5, so you add 5 to each SD, to the right.

35 1SD, 40 2SD, 45 3SD

1 SD 84%, 2 SD 97.5%, 3SD 99%.

Do the second one.

Let me know if my answer was correct.
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#21
03-05-2012
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 653 Threads: 47 Thanked 409 Times in 249 Posts Reputation: 419

Quote:
 Originally Posted by AbSa yupppp the answer is correct but isnt 1SD 68% .... and thanks a lot.... i have been scratching my head on it for past 5 hours
Yes it was difficult for me too, until i started practicing.

Check the cumulative percentages.
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