How to Calculate Sample Variance
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Sample variance is a statistical measure that helps to quantify the degree of dispersion or spread in a set of data. It represents how much the individual data points vary from the mean (average) of the sample. Calculating sample variance is essential for understanding the variability and reliability of your data. In this article, we will provide a step-by-step guide to calculating sample variance.
Step 1: Calculate the mean (average)
Firstly, you need to calculate the average or mean value for your set of data. To find the mean, add all data values together and then divide by the total number of data points (n).
Mean = (Sum of all data values) / (Number of data values)
Example:
Consider a dataset with five numbers: 2, 4, 6, 8, and 10.
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Step 2: Find the difference between each data point and the mean
Next, subtract the mean from each individual data value. This will give you an idea of how much each value deviates from the average.
Example:
(2 – 6) = -4
(4 – 6) = -2
(6 – 6) = 0
(8 – 6) = +2
(10 – 6) = +4
Step 3: Square each difference
To eliminate any negative values, square each difference computed in step two.
Example:
(-4)^2 = 16
(-2)^2 = 4
(0)^2 =0
(+2)^2 =4
(+4)^2=16
Step 4: Sum up squared differences
Add all squared differences obtained in step three.
Example:
16 + 4 + 0 + 4 + 16 = 40
Step 5: Calculate sample variance
To find the sample variance, divide the sum of squared differences from step four by the total number of data points minus one (n – 1). This adjustment (subtracting one) is crucial to correct for bias that occurs when dealing with a sample instead of the whole population.
Sample Variance = (Sum of squared differences) / (Number of data values – 1)
Example:
Sample Variance = 40 / (5 -1) = 40 / 4=10
Having completed these steps, you now have the sample variance. In our example, the sample variance is 10. This value provides insight into the variability within your dataset, allowing you to make informed decisions based on your data analysis. As you become more familiar with these steps, calculating sample variance will become easier and faster, helping you to effortlessly understand and interpret your data’s dispersion.