, , , ,

The mean of a set of numbers is the sum divided by the number of terms.

Simplify the numerator.

Add and .

Add and .

Add and .

Add and .

Divide by .

Convert to a decimal value.

Convert to a decimal value.

Convert to a decimal value.

Convert to a decimal value.

Convert to a decimal value.

The simplified values are .

Set up the formula for standard deviation. The standard deviation of a set of values is a measure of the spread of its values.

Set up the formula for standard deviation for this set of numbers.

Simplify the expression.

Subtract from .

One to any power is one.

Subtract from .

Raise to the power of .

Subtract from .

Raise to the power of .

Subtract from .

Raise to the power of .

Subtract from .

Raising to any positive power yields .

Add and .

Add and .

Add and .

Add and .

Subtract from .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Simplify the numerator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

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.

Find the Standard Deviation 12 , 14 , 5 , 13 , 11