Statistics # Standard Deviation to Variance

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Next, press Solve to find the Variance.

Both Variance and Standard Deviation are Measures of Spread in Statistics.

The Variance is the Sum of the Squared Differences between the given Data and their Mean.

Taking the Square-Root of the Variance then gives the Standard Deviation. The Standard Deviation tells us by how much the data differ from the mean, the average distance from the mean. As formulas:

Say we are given **2,3,4**. Their mean is 3 since **(2+3+4)/3 = 3 **.

The Squared Differences between the data and mean are

** (2-3)² + (3-3)² + (4-3)² = 1+0+1=2 **.

Dividing that by the number of data points, here 3, yields **s²=2/3=0.666 **as the variance.

Finally, take the Square Root of the Variance to find the Standard Deviation
**s= √(s²)=(0.666)=0.81649658092 **.

To find Variance we have to Square the Standard Deviation.

Reason: Standard Deviation is **s **, the Variance is **s²** .

To find Standard Deviation we have to take the Square Root of the Variance.

Reason: The Variance is **s²**, the Square of the Standard Deviation is **s ** .

When computing Population Variance we divide by the Population Size N (as shown in the image above).

When computing Sample Variance we divide by the Sample Size N-1 instead (for technical reasons) .

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