# Relationship between rms and variance

### Difference Between Variance and Standard Deviation (with Comparison Chart) - Key Differences

What is the physical difference between standard deviation and variance? . So, the standard deviation (σ) or root mean square deviation solves that problem. The major difference between variance and standard deviation is that Variance is a numerical value that It is the root mean square deviation. The Root Mean Square Error (RMSE) (also called the root mean square deviation, is a frequently used measure of the difference between values predicted by a CV,RMSE for the resemblance with calculating the coefficient of variance).

You can select class width 0. The graph of MSE is shown to the right of the histogram. A red vertical line is drawn from the x-axis to the minimum value of the MSE function. By Exercise 2, this line intersects the x-axis at the mean and has height equal to the variance.

### Mean, Variance, and Mean Square Error

Thus, this vertical line in the MSE graph gives essentially the same information as the horizontal bar in the histogram. In the applet, construct a frequency distribution with at least 5 nonempty classes and and at least 10 values total.

Compute the min, max, mean and standard deviation by hand, and verify that you get the same results as the applet. Also, explicitly compute a formula for the MSE function. In the applet, set the class width to 0.

Then increase the class width to each of the other four values. More on regression Video transcript - [Instructor] What we're going to do in this video is calculate a typical measure of how well the actual data points agree with a model, in this case, a linear model and there's several names for it. We could consider this to be the standard deviation of the residuals and that's essentially what we're going to calculate.

You could also call it the root-mean-square error and you'll see why it's called this because this really describes how we calculate it. So, what we're going to do is look at the residuals for each of these points and then we're going to find the standard deviation of them. So, just as a bit of review, the ith residual is going to be equal to the ith Y value for a given X minus the predicted Y value for a given X. Now, when I say Y hat right over here, this just says what would the linear regression predict for a given X?

And this is the actual Y for a given X. So, for example, and we've done this in other videos, this is all review, the residual here when X is equal to one, we have Y is equal to one but what was predicted by the model is 2. The average deviation of a signal is found by summing the deviations of all the individual samples, and then dividing by the number of samples, N. Notice that we take the absolute value of each deviation before the summation; otherwise the positive and negative terms would average to zero.

The average deviation provides a single number representing the typical distance that the samples are from the mean. While convenient and straightforward, the average deviation is almost never used in statistics.

This is because it doesn't fit well with the physics of how signals operate. In most cases, the important parameter is not the deviation from the mean, but the power represented by the deviation from the mean.

For example, when random noise signals combine in an electronic circuit, the resultant noise is equal to the combined power of the individual signals, not their combined amplitude.

The standard deviation is similar to the average deviation, except the averaging is done with power instead of amplitude.

To finish, the square root is taken to compensate for the initial squaring. In equation form, the standard deviation is calculated: In the alternative notation: Notice that the average is carried out by dividing by N - 1 instead of N. This is a subtle feature of the equation that will be discussed in the next section. The standard deviation is a measure of how far the signal fluctuates from the mean. The variance represents the power of this fluctuation.

## Standard deviation of residuals or Root-mean-square error (RMSD)

Another term you should become familiar with is the rms root-mean-square value, frequently used in electronics. By definition, the standard deviation only measures the AC portion of a signal, while the rms value measures both the AC and DC components.

**Calculating RMS Noise to Peak-to-Peak Noise**

If a signal has no DC component, its rms value is identical to its standard deviation.