Curve 1 has st. dev. 1, Curve 2 has st. dev. of 5: add curve

[thegreatescape333]

It's been a long time since I've used the probability/stats that I learned in college. I would appreciate help getting an intuitive understanding of how the standard deviation and variance of a curve change as more data is added. For example, say you have two normal curves, both with the same mean. Curve 1 has a standard deviation of 1 and curve 2 has a standard deviation of 5. What happens when you add the data from Curve 1 and Curve 2 to get Curve 3?

?1 = 1
?2 = 5
?3 = ??

Is there an easy way to calculate the standard deviation and variance or curve 3 if the populations of curve 1 and 2 are the same? Is there a general rule if the populations of curve 1 and 2 are different?

I am told that the std dev wil increase in this case, but I don't understand the reasoning behind that answer.... For example, if you add a normal curve with std dev of 1 to a normal curve with a std dev of 100, you have essentially increased the proportion of data near the mean, right? If one standard deviation extended both directions from the mean is supposed to include 68% of the data, wouldn't the standard deviation have to decrease? I'm pretty confused with this, any explaination would be greatly appreciated! Also, if you know of a website where I can read up on this more it would help.

Thanks,
Rebecca

 

[royhaas]

Re: Standard Deviation and Variance Review

The variances add if the two populations are independent. In other words, \(\displaystyle \sigma_3^2 = \sigma_1^2+\sigma_2^2\).

 

[thegreatescape333]

Re: Standard Deviation and Variance Review

Is there anywhere online that you know of where I can read more about this? As I said, it doesn't make sense to me that the var and std dev would increase... I have seen this formula before but have no idea where it's coming from.

Thanks,
Rebecca