# Statistics Examples

Find the Sample Standard Deviation
, , , , , ,
Step 1
Find the mean.
Step 1.1
The mean of a set of numbers is the sum divided by the number of terms.
Step 1.2
Simplify the numerator.
Step 1.2.1
Step 1.2.2
Step 1.2.3
Step 1.2.4
Step 1.2.5
Step 1.2.6
Step 1.3
Divide by .
Step 2
Simplify each value in the list.
Step 2.1
Convert to a decimal value.
Step 2.2
Convert to a decimal value.
Step 2.3
Convert to a decimal value.
Step 2.4
Convert to a decimal value.
Step 2.5
Convert to a decimal value.
Step 2.6
Convert to a decimal value.
Step 2.7
Convert to a decimal value.
Step 2.8
The simplified values are .
Step 3
Set up the formula for sample standard deviation. The standard deviation of a set of values is a measure of the spread of its values.
Step 4
Set up the formula for standard deviation for this set of numbers.
Step 5
Simplify the result.
Step 5.1
Simplify the expression.
Step 5.1.1
Subtract from .
Step 5.1.2
Raise to the power of .
Step 5.1.3
Subtract from .
Step 5.1.4
Raise to the power of .
Step 5.1.5
Subtract from .
Step 5.1.6
Raise to the power of .
Step 5.1.7
Subtract from .
Step 5.1.8
Raising to any positive power yields .
Step 5.1.9
Subtract from .
Step 5.1.10
Raise to the power of .
Step 5.1.11
Subtract from .
Step 5.1.12
Raise to the power of .
Step 5.1.13
Subtract from .
Step 5.1.14
Raise to the power of .
Step 5.1.15
Step 5.1.16
Step 5.1.17
Step 5.1.18
Step 5.1.19
Step 5.1.20
Step 5.1.21
Subtract from .
Step 5.2
Cancel the common factor of and .
Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factors.
Step 5.2.2.1
Factor out of .
Step 5.2.2.2
Cancel the common factor.
Step 5.2.2.3
Rewrite the expression.
Step 5.3
Rewrite as .
Step 5.4
Simplify the numerator.
Step 5.4.1
Rewrite as .
Step 5.4.1.1
Factor out of .
Step 5.4.1.2
Rewrite as .
Step 5.4.2
Pull terms out from under the radical.
Step 5.5
Multiply by .
Step 5.6
Combine and simplify the denominator.
Step 5.6.1
Multiply by .
Step 5.6.2
Raise to the power of .
Step 5.6.3
Raise to the power of .
Step 5.6.4
Use the power rule to combine exponents.
Step 5.6.5
Step 5.6.6
Rewrite as .
Step 5.6.6.1
Use to rewrite as .
Step 5.6.6.2
Apply the power rule and multiply exponents, .
Step 5.6.6.3
Combine and .
Step 5.6.6.4
Cancel the common factor of .
Step 5.6.6.4.1
Cancel the common factor.
Step 5.6.6.4.2
Rewrite the expression.
Step 5.6.6.5
Evaluate the exponent.
Step 5.7
Simplify the numerator.
Step 5.7.1
Combine using the product rule for radicals.
Step 5.7.2
Multiply by .
Step 6
The standard deviation 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.