Statistics Examples

, , , , ,
Step 1
The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.
Step 2
Simplify the result.
Tap for more steps...
Step 2.1
Simplify the expression.
Tap for more steps...
Step 2.1.1
One to any power is one.
Step 2.1.2
Raise to the power of .
Step 2.1.3
Raise to the power of .
Step 2.1.4
Raise to the power of .
Step 2.1.5
Raise to the power of .
Step 2.1.6
Raise to the power of .
Step 2.1.7
Add and .
Step 2.1.8
Add and .
Step 2.1.9
Add and .
Step 2.1.10
Add and .
Step 2.1.11
Add and .
Step 2.2
Cancel the common factor of and .
Tap for more steps...
Step 2.2.1
Rewrite as .
Step 2.2.2
Cancel the common factors.
Tap for more steps...
Step 2.2.2.1
Rewrite as .
Step 2.2.2.2
Cancel the common factor.
Step 2.2.2.3
Rewrite the expression.
Step 2.3
Rewrite as .
Step 2.4
Multiply by .
Step 2.5
Combine and simplify the denominator.
Tap for more steps...
Step 2.5.1
Multiply by .
Step 2.5.2
Raise to the power of .
Step 2.5.3
Raise to the power of .
Step 2.5.4
Use the power rule to combine exponents.
Step 2.5.5
Add and .
Step 2.5.6
Rewrite as .
Tap for more steps...
Step 2.5.6.1
Use to rewrite as .
Step 2.5.6.2
Apply the power rule and multiply exponents, .
Step 2.5.6.3
Combine and .
Step 2.5.6.4
Cancel the common factor of .
Tap for more steps...
Step 2.5.6.4.1
Cancel the common factor.
Step 2.5.6.4.2
Rewrite the expression.
Step 2.5.6.5
Evaluate the exponent.
Step 2.6
Simplify the numerator.
Tap for more steps...
Step 2.6.1
Combine using the product rule for radicals.
Step 2.6.2
Multiply by .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Enter YOUR Problem
Mathway requires javascript and a modern browser.