Statistics How To

How to Find Sample Variance in Statistics

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How to Find Sample Variance: Overview

How to Find Sample Variance in Statistics.

Variance tells you how spread out a data set is.


The sample variance is one measure of the spread of data. The sample variance gives you an idea of how much your sample differs from the average population. By itself, the variance isn’t really a meaningful number. Technically, the variance is used to determine the “error bound” for estimates. But it’s an essential step in calculating the standard deviation. You can calculate sample variance using technology (see the links at the bottom of the article), or you can calculate it by hand.
Watch the video, which explains how to find sample variance and standard deviation. Or read the steps below:

How to Find Sample Variance: Steps

Variance formula = s2 = Σ(X-Xbar)2 / (n-1)

Sample Question: Find the sample variance for the following data set: 1245,1255,1654,1547,1787,1989,1878,2011,2145,2545,2656.

Step 1: Add up all of the numbers in your data set:
1245 + 1255 + 1547 + 1654 + 1787 + 1878 + 1989 + 2011 + 2145 + 2545 + 2656 = 20712

Step 2: Square the number you found in Step 1:
20712 x 20712 = 428986944
…and then divide by the number of items on your data set.
428986944 / 11 = 38998813.09090909
Set this number aside for a moment.

Step 3: Square all of the numbers in your data set and then add them together.
(1245 x 1245) + (1255 x 1255) + (1547 x 1547) + (1654 x 1654) + (1787 x 1787) + (1878 x 1878) + (1989 x 1989) + (2011 x 2011) + (2145 x 2145) + (2545 x 2545) + (2656 x 2656) = 41106856

Step 4: Subtract the number you calculated in Step 2 from the number you calculated in Step 3:
41106856 – 38998813.09090909 = 2108042.9090909064

Step 5: Subtract 1 from the number of items in your data set:
11 – 1 = 10.

Step 6: Divide the number you calculated in step 4 by the number you calculated in step 5:
2108042.9090909064 / 10 = 210804.29090909063
This is the Variance.

That’s it!

Tip: Use our Online Sample variance and standard deviation calculator. to check your work. It doesn’t just give you the answer, it walks you through the exact numbers for each step, so you can check your work at each step of the problem.

Related articles:
Find variance on a TI-83 graphing calculator.
Find variance on a TI-89 graphing calculator.
Calculate sample variance in Excel.

Check out our YouTube channel for more stats help and tips!

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