Statistics Examples

Find the Quadratic Mean (RMS) 2 , 4 , 6 , 8 , 10 , 12
, , , , ,
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.
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Step 2.1
Simplify the expression.
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Step 2.1.1
Raise to the power of .
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 .
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Step 2.2.1
Factor out of .
Step 2.2.2
Cancel the common factors.
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Step 2.2.2.1
Factor out of .
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.
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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 .
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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 .
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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.
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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:
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