This subpage of the Data Analysis page displays basic summary statistics computed from the individual trend data values from the Data Entry Subpage.
Values button 
Show summary statistics for raw data values 
Residuals button 
Show summary statistics for the residuals from the linear regression trend line. 
Location droplist 
Select location (or all locations) for which to show summary statistics. 
Season droplist 
Select season (for Seasonal Kendall design) for which to show summary stats. 
\(n\) 
is the number of measurements in a data set 
Min 
is the minimum of the \(n\) data 
Max 
is the maximum of the \(n\) data 
Range 
is the minimum value minus the maximum value, i.e., \( Range = x_{[n]}  x_{[1]} \) 
Mean 
is the arithmetic mean computed as: \( \bar x= \frac{1}{n} \displaystyle\sum\limits_{i=1}^n x_i \) 
Median 
is the 50th percentile of the data set, i.e., the value above which and below which half the data set lies. The sample median is computed from the ordered data (order statistics) \( x_{[1]} \leq x_{[2]} \leq \dotsb \leq x_{[n]} \) as follows: Median = \( x_{[(n+1)/2]} \) if \(n\) is an odd number Median = \( \frac{1}{2} (x_{[n/2]} + x_{[(n+2)/2]}) \) if \(n\) is an even number 
Variance 
is computed as: \( Var = s^2 \) (see below) 
Standard Deviation 
is computed as: \( s = \sqrt{ \frac{1}{n1} \displaystyle\sum\limits_{i=1}^n (x_i  \bar x)^2} \) 
Standard Error 
is the standard deviation of the estimated mean. It is computed as: \( SE = \frac{s}{ \sqrt{n}} = \sqrt{ \frac{1}{n(n1)} \displaystyle\sum\limits_{i=1}^n (x_i  \bar x)^2} \) 
Interquartile Range 
is the 75th percentile of the data set minus the 25th percentile of the data set 
Skewness 
Is a measure of the symmetry of the data set. It is computed as: \( SKEW = \frac{ \frac{n}{(n1)(n2)} \displaystyle\sum\limits_{i=1}^n (x_i  \bar x)^3}{s^3} \) where \( \bar x \) and s are computed as given above. 
\(P\)th Percentile 
is the value below which \(p\)% of the \(n\) data fall and above which (100  \(p\))% of the \(n\) data fall. The \(P\)th percentile is computed in VSP by first computing \(k\) = \(p\)(\(n\)+1). If \(k\) is an integer, the \(P\)th percentile is \( x_{[k]} \) , which is the \(K\)th largest of the \(n\) data values. For example, to compute the 50th percentile of a data set of \(n\) = 9 measurements, we have \(p\) = 0.50 and \(k\) = \(p\)(\(n\)+1) = 0.50(10) = 5, which is an integer. Hence, the 50th percentile (the median) is the 5th largest datum, \( x_{[5]} \) . If \(k\) is not an integer, the \(P\)th percentile is obtained by linear interpolation between the two closest order statistics. For example if \(n\) = 11 and \(p\) = 0.70, then \(k\) = \(p\)(\(n\)+1) = 0.70(12) = 8.4, then the 70th percentile is found by linear interpolation between the 8th and 9th largest of the 11 data, i.e., between \( x_{[8]} \) and \( x_{[9]} \). 
Normal Distribution Test 

Significance Level 
Choose a 1%, 5%, or 10% significance level for the associated normality test. 

VSP conducts a ShapiroWilk normality test if there are fewer than 50 selected data values; otherwise a Lilliefors normality test is conducted. 
Conover, W.J. 1999. Practical Nonparametric Statistics, 3rd edition, Wiley, NY.
Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Monitoring, Wiley, NY.
ProUCL. 2004. ProUCL Version 3.0 User Guide April 2004. Available for download from http://www.epa.gov/nerlesd1/tsc/tsc.htm