Is there an equation to find the standard deviation of a list deterministic-ally?

Question

Say I have many lists of random number between 0 and 10 inclusive, and this list has 100 values.

the lists will look something like this:

• [9 9 4 7 0 5 8 3 ... 1 9 2 5 6 6 4 2 0 1 9 8]
• [6 0 1 8 6 9 6 4 ... 6 4 3 10 9 2 3 0 3 1 3 10]
• [0 9 2 5 6 7 8 8 ... 0 4 1 7 5 9 2 2 3 6 1 9]

the average value of this list will be close to 5. Is there an equation to find the standard deviation without going through the whole sum((distancetomean)^2) etc...

Answer 1

If you need to find standard deviations of a lot of datasets of this kind, you should consider using a statistical calculator that is programmed to find SDs, or using statistical software.

R is excellent software and free from www.r-project.org. Just follow the path to install R on your Windows, Mac, or UNIX computer.

The package is extensive and some of the explanations may seem technical.

But here how to find the standard deviation of a list. First, use c-notation and commas to enter the data. Proofread, give the data vector a name, for example x and then type sd(x).

 x = c(1,5,6,7,3,4,9,7)
 sd(x)
 [1] 2.54951

The [1] in brackets just indicates the answer.

While, you're at it, you can find the variance, mean, and median.

 > var(x)
 [1] 6.5
 > mean(x)
 [1] 5.25
 > median(x)
 [1] 5.5

However, there is no way to get around using a messy formula to get the standard deviation. When you use R, the software is just using the formula for you.