Quadratic Mean The quadratic mean (or root mean square, or R.M...

Question

Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:

Quadratic mean = sqrt(∑x^2/n)

Find the R.M.S. of these voltages measured from household current: 0, 60, 110, 0. How does the result compare to the mean?

Quadratic mean = sqrt(∑x^2/n)

Find the R.M.S. of these voltages measured from household current: 0, 60, 110, 0. How does the result compare to the mean?

Accepted Answer

Welcome back, everyone. The root mean square. RMS, also known as the quadratic mean, is computed by using the following formula RMS equals square root of the sum of X2 divided by M. Find the RMS speed of a vehicle. Recorded at different times 30 kilometers per hour, 50 kilometers per hour, 70 kilometers per hour, and 90 kilometers per hour. How does the result compare to the arithmetic mean? So first of all, let's identify RMS. The root means square. We're going to take square root off. And now it says in the numerator that we're adding X2. This means that for every data point we have to square it, right, and we have to add all of those squares. So we're taking 30 kilometers per hour squared. We're adding 50 kilometers per hour squared. 70 kilometers per hour squared. And then 90 kilometers per hour squared. We have to divide that by M, so we have 4 data points. This means that we're dividing by 4. When we perform the calculations, we're going to get 64.03 kilometers per hour, so that's our first answer to this problem. Now we want to compare this result to the arithmetic means, so let's identify. The arithmetic mean, which is basically the sum of X divided by Ns, we have to add those values. 30 kilometers per hour. Plus 50 kilometers per hour. Plus 70 kilometers per hour plus 90 kilometers per hour, and we have to divide by N which is once again 4. We're going to get 60 kilometers per hour. And now we can compare, we can say that RMS, the root mean square, is Slightly higher Because we have 64.03 kilometers per hour for RMS and we have a slightly smaller number for the arithmetic mean, that's 60 kilometers per hour. And that's it. We have our answers. Thank you for watching.

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Key Concepts

Quadratic Mean (Root Mean Square)

Calculation of R.M.S.

Comparison with Arithmetic Mean

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