Standard Deviation?

Question

How do you find the sd of something that only gives you two or three numbers?

Answer 1

The first thing you would do is find the mean (average) of the numbers. Then you would subtract the mean from each of the numbers in a sample, square each result, add up all the results together, divide by the number of numbers in the sample, and then take the square root of that.

That's probably hard to follow, so let me give you the formula of standard deviation and then a simple example.

X = number in the sample, Standard deviation = σ, Mean = μ, Σ = "the sum of", N = the number of numbers in the sample

σ = sqrt[Σ(X - μ)² / N]


So, let's say you're going to find the standard deviation of the sample {1, 2, 3}.

The mean μ = (1 + 2 + 3)/(3) = 2
N = 3 (three numbers in the sample)

To find Σ(X - μ)² :
X = 1, 2, 3
X - μ = (1-2), (2-2), (3-2)
(X - μ)² = (-1)², (0)², (1)²
Σ(X - μ)² = 1 + 0 + 1 = 2

And σ² = Σ(X - μ)² / N = 2/3
σ² = 2/3

σ² is called the "variance", the standard deviation is the square root of the variance, so take the square root of both sides and you get...

σ = sqrt[2/3] = 0.816496581...

Therefore, σ (the standard deviation) in the example is about equal to 0.816.

Hope this helps. Best of luck.

Answer 2

By definition, to do statistics all you need is a sample size greater than one. Even if your sample size is very small (around 2), you can still characterize it using the standard statistical techniques. It's just that your predictability becomes unreliable.

If you look at the standard devation formula in the link I gave, all that is necessary is the number of elements, the average of the elements, and the individual elements. If you have two or three numbers, those criteria are fully satisfied.