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.
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.
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.
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.
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.