Statistics How To

The variance and standard deviations of samples are ways to measure the spread—or variability—of a sample or how far away from the “norm” a result is. In order to determine standard deviation, you have to find the variance first; standard deviation is just the square root of variance. The variance formula can be tricky to use—especially if you are rusty on order of operations. By far the easiest way to find the variance and standard deviation is to use an online calculator . However, if you don’t have internet access when you are working these problems, here is how to find the variance and standard deviation of a sample in a few short Steps.

Step 1: Add up the numbers in your given data set. For example, let’s say you were given a set of data for trees in California (heights in feet):

3, 21, 98, 203, 17, 9

Add them together:

3 + 21 + 98 + 203 + 17 + 9 = 351

Step 2: Square your answer:

351 × 351 = 123,201

…and divide by the number of items in your data set. We have 6 items in our example so:

123,201 / 6 = 20,533.5

Set this number aside for a moment.

Step 3: Take your set of original numbers from Step 1, and square them individually this time:

3 × 3 + 21 × 21 + 98 × 98 + 203 × 203 + 17 × 17 + 9 × 9

Add those numbers (the squares) together:

9 + 441 + 9604 + 41209 + 289 + 81 = 51,633

Step 3: Subtract the amount in Step 2 from the amount in Step 3.

51,633 – 20,533.5 = 31,099.5

Set this number aside for a moment.

Step 5: Subtract 1 from the number of items in your data set. For our example:

6 – 1 = 5

Step 6: Divide the number in Step 4 by the number in Step 5:

31,099.5 / 5 = 6,219.9

Step 7: Take the square root of your answer from Step 6. This gives you the standard deviation:

√6,219.9 = 78.86634

Related posts:

1. How to Find a Sample Size Given a Confidence Interval and Width (Known Standard Deviation)
2. The Easy Way to Find the Variance on a TI-89 Calculator
3. How to Find a Standard Deviation on a TI 83 Calculator
4. Standard deviation: binomial distribution
5. How to Find a Variance on a TI 83 Calculator