Calculate the quadratic mean of the following set of numbers: 2, 4, 6, 8.

Question

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The problem asks to calculate the quadratic mean (Root Mean Square, RMS) for the set of numbers $2, 4, 6, 8$ . The formula for RMS is given as $\text{RMS} = \sqrt{\frac{\sum x^2}{n}}$ .

Identify the given numbers and the count.
The numbers are $x = \{2, 4, 6, 8\}$ .
The count of numbers is $n = 4$ .
Calculate the square of each number.
$2^2 = 4$
$4^2 = 16$
$6^2 = 36$
$8^2 = 64$
Sum the squares of the numbers.
$\sum x^2 = 4 + 16 + 36 + 64 = 120$
Substitute the sum of squares and the count into the RMS formula.
$\text{RMS} = \sqrt{\frac{120}{4}}$
Simplify the expression under the square root.
$\text{RMS} = \sqrt{30}$
Calculate the square root.
$\text{RMS} \approx 5.477$
The Root Mean Square for the given set of numbers is:
$5.477$

Calculate the quadratic mean of the following set of numbers: 2, 4, 6, 8.

Answer

Step-by-step solution

Identify the given numbers and the count.

Calculate the square of each number.

Sum the squares of the numbers.

Substitute the sum of squares and the count into the RMS formula.

Simplify the expression under the square root.

Calculate the square root.

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