RPinPA said:##<(x_1 - x_2)^2> = <x_1^2 - 2x_1x_2 + x_2^2 > = <x_1^2> - 2<x_1 x_2> + <x_2^2>## and similarly for ##<(x_3 - x_1)^2>## and ##<(x_2 - x_3)^2>##.
That should give you a clue on how to combine them to get your desired result, but you need to know something about the cross terms like ##<x_1 x_2>##. You didn't tell us what these variables are, but information you have on them will probably tell you what those terms are (perhaps 0).
I'm just guessing here. I don't know what it is you're trying to get or what you've tried and why you didn't get the desired result. Perhaps show your work so far?
A mean square average is a statistical measure that represents the average of the squared differences between a set of values and their mean. It is commonly used to measure the variability or dispersion of a data set.
To calculate a mean square average, you first need to find the mean of the data set by adding all the values and dividing by the total number of values. Then, for each value in the data set, subtract the mean and square the result. Finally, add all the squared differences and divide by the total number of values to get the mean square average.
The mean represents the average value of a data set, while the mean square average takes into account the variability or dispersion of the data set by squaring the differences between each value and the mean. In other words, the mean square average provides a more comprehensive measure of the data set.
A mean square average is typically used when analyzing data sets that have a wide range of values or when comparing data sets with different units of measurement. It is also commonly used in statistical analysis and in fields such as finance, engineering, and physics.
No, a mean square average cannot be negative. Since the squared differences between values and their mean are always positive, the mean square average will always be a positive value.