Instruction of online calculator

Variance of the Data

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Input Data
Output

Understanding Variance

Variance is a statistical measure that represents the spread or dispersion of data points in a dataset. It tells us how much the individual data points differ from the mean (average) of the dataset. A small variance indicates that the data points are closely clustered around the mean, while a large variance suggests a wider spread of values.

The formula for variance is as follows:

  • Population Variance (σ²):

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  • Sample Variance (s²):

Numerical Example

Let’s calculate the variance for a small dataset of numbers:
Dataset: [4, 8, 6, 5, 3]

Step 1: Calculate the Mean
Mean ((\bar{x})) = ( \frac{4 + 8 + 6 + 5 + 3}{5} = 5.2 )

Step 2: Find the Squared Differences from the Mean

  • ( (4 – 5.2)^2 = 1.44 )
  • ( (8 – 5.2)^2 = 7.84 )
  • ( (6 – 5.2)^2 = 0.64 )
  • ( (5 – 5.2)^2 = 0.04 )
  • ( (3 – 5.2)^2 = 4.84 )

Step 3: Calculate the Variance
Variance ((s^2)) = ( \frac{1.44 + 7.84 + 0.64 + 0.04 + 4.84}{5} = 2.96 )

Thus, the variance for this dataset is 2.96. In the following, you can see the detail of calculation in the table.

for the sample variance, we have the following table.

Using the Calculator

Here’s how you can calculate variance using a standard calculator:

  1. Input the data values: Enter all the numbers one by one into your calculator.
  2. Get the variance: For population variance, divide the sum of squared differences by the number of data points. For sample variance, divide by the number of data points minus one.