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Basic Math Examples
,
Step 1
Step 1.1
Factor out of .
Step 1.2
Cancel the common factors.
Step 1.2.1
Factor out of .
Step 1.2.2
Cancel the common factor.
Step 1.2.3
Rewrite the expression.
Step 2
Step 2.1
Factor out of .
Step 2.2
Cancel the common factors.
Step 2.2.1
Factor out of .
Step 2.2.2
Cancel the common factor.
Step 2.2.3
Rewrite the expression.
Step 3
The mean of a set of numbers is the sum divided by the number of terms.
Step 4
Step 4.1
Combine the numerators over the common denominator.
Step 4.2
Add and .
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Step 6.1
Factor out of .
Step 6.2
Cancel the common factor.
Step 6.3
Rewrite the expression.
Step 7
Divide.
Step 8
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 9
Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.
Step 10
Set up the formula for variance for this set of numbers.
Step 11
Step 11.1
Simplify the numerator.
Step 11.1.1
To write as a fraction with a common denominator, multiply by .
Step 11.1.2
Combine and .
Step 11.1.3
Combine the numerators over the common denominator.
Step 11.1.4
Simplify the numerator.
Step 11.1.4.1
Multiply by .
Step 11.1.4.2
Subtract from .
Step 11.1.5
Divide by .
Step 11.1.6
Raise to the power of .
Step 11.1.7
To write as a fraction with a common denominator, multiply by .
Step 11.1.8
Combine and .
Step 11.1.9
Combine the numerators over the common denominator.
Step 11.1.10
Simplify the numerator.
Step 11.1.10.1
Multiply by .
Step 11.1.10.2
Subtract from .
Step 11.1.11
Divide by .
Step 11.1.12
Raise to the power of .
Step 11.1.13
Add and .
Step 11.2
Simplify the expression.
Step 11.2.1
Subtract from .
Step 11.2.2
Divide by .
Step 12
Approximate the result.