Solved – Standard deviation of a dichotomous variable

Suppose, I have a dichotomous variable – gender:

Male coded as 0 Female coded as 1

Frequency of male – 30 Frequency of female – 20

The mean of a dichotomous variable is just the proportion which has been coded as 1. So, in this case, I believe it is 30/50.

The confusing part is while solving for standard deviation. How can I do that? Also, is the answer a meaningful one?

If you code males as 0 and females as 1, the mean will be $frac{20}{50}$, not $frac{30}{50}$.

For the SD, just use the standard formula with your coding, $x_iin{0,1}$ and the mean $frac{20}{50}$ you calculated above.

No, I don't think this answer is meaningful. In reporting the mean and SD, we summarize a distribution in two numbers. If we have a binary distribution, we have a much easier and more intuitive way of summarizing it in two numbers: just report the numbers of males and females.

Similar Posts:

Rate this post

Leave a Comment