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### The Ever-confusing Statistical Terms

To illustrate the different statistical terms we usually run into when we discuss data accuracy, let us consider the five error values (3-in., 2-in, 1-in., 5-in., and 4-in.) that were calculated on a population of data.

**Mean**(average) $=\frac{3+2+1+5+4}{5}=3.0$**Range**= the distance between the largest error and the smallest error, i.e. Smallest = 1, Largest = 5 3)**Variance**= measure of spread or dispersion around the mean. It is the mean square of all the errors $=\left({\left(3-3\right)}^{2}+{\left(2-3\right)}^{2}+{\left(1-3\right)}^{2}+{\left(5-3\right)}^{2}+{\left(4-3\right)}^{2}\right)\frac{1}{5-1}=\frac{0+1+4+4+1}{4}=\frac{10}{4}=2.5inc{h}^{2}$

Here,*inch*is a meaningless unit and a better statistical term to use is the standard deviation.^{2}**Standard deviation, also called one-sigma,**is the square root of the variance = $=\surd 2.5=1.581inch\left(\text{issamplemean}\right)$**Root Mean Square Error (RMSE)**- RMSE is not Standard deviation or sigma; they are different.
- Root Mean Square Error (RMSE) is computed as follows:

$RMSE\text{}=\text{}\surd \text{}\left(\Sigma {\left(\text{}Z\text{}\u2013\text{}{Z}_{i}\right)}^{2}/\text{}n\right)$

Where,

Z = Measured Value from the data

Z_{i }= Control Value (field surveyed)

n = number of measurements