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
| Numbers | Mean deviation |
| 15 | –6 |
| 11 | –2 |
| 8 | 1 |
| 3 | 6 |
| 13 | –4 |
| 8 | 1 |
| 5 | 4 |
STEP 2.
Square each mean deviation
| MD | MD² |
| (–6)² | 36 |
| (–2)² | 4 |
| (1)² | 1 |
| (6)² | 36 |
| (–4)² | 16 |
| (1)² | 1 |
| (4)² | 16 |
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}=15.71Final answer
The variance of the following numbers:
15, 11, 8, 3, 13, 8, 5
= 15.71
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