Question

Currently, I have the following information

1. Standard deviation = 1.6667
2. Size of set = 4
3. Average = 2.5

From the following number set A : {1, 2, 3, 4}

1. Standard deviation = 1.6667
2. Size of set = 4
3. Average = 1.5

From the following number set B : {0, 1, 2, 3}

Now, I do not have the detailed element information in both set A and set B. I do not know set A is having {1, 2, 3, 4}. I also do not know set B is having {0, 1, 2, 3}.

What I only know is, the Standard deviation, Size of set and Average for set A and B.

Now, I would like to compute the Standard deviation for the combination of set A and set B. (Of course, there should be no problem in computing Size of set and Average of set A and set B). Is it possible to do so?

Answer 1

1. Do you mean variance? The standard deviation is just the square root of the variance.
2. The variance of these sets is 5/4, not 5/3.
3. The unbiased sample estimate of these sets is 5/3.

Anyway, if you have the mean and variance (or unbiased sample estimate) of a set, then you can get the sum of squares just by multiplying by n (resp. n-1). So you can get the sum of squares over A and B. Then just use the fact that the variance is equal to the mean of the squares minus the square of the mean.