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#1
02-18-2018, 02:08 PM
 Steven Estes Guest Join Date: Sep 2001 Posts: 69
Can you put two different normal curves together and get a normal curve?

Can you put together two (different) normal curves and get a normal curve? I
tried it with male and female heights, experimenting with different
mean-median-modes. The best I could get was a plateau.
#2
02-18-2018, 02:14 PM
 OldGuy Charter Member Join Date: Dec 2002 Location: Very east of Foggybog, WI Posts: 4,634
No. If you have two independent normal random variables with different means or variances, then the mixture is not normal. The density function (or histogram) will be a weighted average of the two. Generally it will have two modes.
#3
02-18-2018, 02:15 PM
 Maserschmidt Guest Join Date: May 2009 Location: New England Posts: 5,440
I'm not 100% sure what you're describing, but the sum of two independent normally distributed random variables does create a new normal distribution.

ETA: I see Old Guy's response...I thought the sum of normals was itself normal...oh well.

Last edited by Maserschmidt; 02-18-2018 at 02:16 PM.
#4
02-18-2018, 02:15 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 75,164
Depends on what you mean by "put together". If you have one population with one normal distribution of some trait, and another with a different distribution, (like male and female heights), then no, you won't get a normal curve unless the two distributions happen to be identical. On the other hand, if you draw a number from one normal distribution, and then draw another number from a different normal distribution, and add them together, then the distribution of the sums will always be a normal distribution. In fact, whenever you do this with any two distributions that meet a few criteria, the result will be closer to a normal distribution than either of the originals was.
#5
02-18-2018, 03:12 PM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,223
Quote:
 Originally Posted by Maserschmidt I'm not 100% sure what you're describing, but the sum of two independent normally distributed random variables does create a new normal distribution. ETA: I see Old Guy's response...I thought the sum of normals was itself normal...oh well.
You're correct - the distribution of the sum of two normal distributions is a normal distribution. But the sum of two normal distributions isn't a normal distribution.

So if men's heights and women's heights are each normal distributions with different averages, the total (i.e. distribution of men and women) isn't a normal distribution. But the distribution of married couples' combined heights (i.e. the added height of each couple) is a normal distribution.

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