Finding The Variance Of Numbers

Finding the variance of numbers is a compulsory step before you can find the standard deviation in statistics.

In this lesson, you will learn the formula and the step-by-step method for finding the variance of numbers.

BONUS: A link to practice questions on statistics is included at the end of this lesson.

Formula for finding the variance of numbers

The formula for finding the variance of numbers is to square the mean deviation of all the numbers and then find their average mean.

\frac {(MD)²+(MD)²+(MD)²...}{n}

Where:

  • MD = Mean Deviation
  • n = total number

Question on finding the variance of numbers

Let’s take an example:

Question

Find the variance of the following numbers:

15, 11, 8, 3, 13, 8, 5

STEP 1.

Find the mean deviation of each number

NumbersMean deviation
15–6
11–2
81
36
13–4
81
54

STEP 2.

Square each mean deviation

MDMD²
(–6)²36
(–2)²4
(1)²1
(6)²36
(–4)²16
(1)²1
(4)²16

STEP 3.

Find the mean of your squared mean deviations

\frac{36+4+1+36+16+1+16}{7}
  • Add the squared mean deviations
\frac{110}{7}
  • Divide by their total number
\frac{110}{7}=15.71

Final answer

The variance of the following numbers:

15, 11, 8, 3, 13, 8, 5

= 15.71

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