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 4: 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. This gives you the variance:
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
