Finite Math Examples

Find the Variance 5 , 10 , 19 , 22 , 16 , 13 , 8 , 17
, , , , , , ,
Step 1
The mean of a set of numbers is the sum divided by the number of terms.
Step 2
Simplify the numerator.
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Step 2.1
Add and .
Step 2.2
Add and .
Step 2.3
Add and .
Step 2.4
Add and .
Step 2.5
Add and .
Step 2.6
Add and .
Step 2.7
Add and .
Step 3
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factors.
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factor.
Step 3.2.3
Rewrite the expression.
Step 4
Divide.
Step 5
The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.
Step 6
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
Step 7
Set up the formula for variance for this set of numbers.
Step 8
Simplify the result.
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Step 8.1
Simplify the numerator.
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Step 8.1.1
Subtract from .
Step 8.1.2
Raise to the power of .
Step 8.1.3
Subtract from .
Step 8.1.4
Raise to the power of .
Step 8.1.5
Subtract from .
Step 8.1.6
Raise to the power of .
Step 8.1.7
Subtract from .
Step 8.1.8
Raise to the power of .
Step 8.1.9
Subtract from .
Step 8.1.10
Raise to the power of .
Step 8.1.11
Subtract from .
Step 8.1.12
Raise to the power of .
Step 8.1.13
Subtract from .
Step 8.1.14
Raise to the power of .
Step 8.1.15
Subtract from .
Step 8.1.16
Raise to the power of .
Step 8.1.17
Add and .
Step 8.1.18
Add and .
Step 8.1.19
Add and .
Step 8.1.20
Add and .
Step 8.1.21
Add and .
Step 8.1.22
Add and .
Step 8.1.23
Add and .
Step 8.2
Simplify the expression.
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Step 8.2.1
Subtract from .
Step 8.2.2
Divide by .
Step 9
Approximate the result.