# Can you put two different normal curves together and get a normal curve? **URL:** \ **Category:** Factual Questions\ **Created:** [February 18, 2018, 8:08pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076 "2018-02-18T20:08:21Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Steven\_Estes](https://avatars.discourse-cdn.com/v4/letter/s/94ad74/32.png) [@Steven\_Estes](https://boards.straightdope.com/u/Steven_Estes)\ **Post date:** [February 18, 2018, 8:08pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076/1 "2018-02-18T20:08:21Z")
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. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [February 18, 2018, 8:14pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076/2 "2018-02-18T20:14:01Z")
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. ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [February 18, 2018, 8:15pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076/3 "2018-02-18T20:15:28Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 18, 2018, 8:15pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076/4 "2018-02-18T20:15:41Z")
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. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [February 18, 2018, 9:12pm UTC](https://boards.straightdope.com/t/can-you-put-two-different-normal-curves-together-and-get-a-normal-curve/809076/5 "2018-02-18T21:12:55Z")
> [@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.