# MagicPlot Manual

Plotting and nonlinear fitting software

statistics

# Differences

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 statistics [Mon May 28 17:09:12 2012]Alexander statistics [Sun Nov 8 12:21:24 2015] Line 1: Line 1: - ====== Descriptive Statistics (Pro edition only) ====== - Select ''​Tools -> Statistics''​ menu item to open the statistics dialog. Statistics dialog shows statistics on currently selected table columns or curves on plot. The statistics is updated every time you activate different windows or change the selection in active window. Select multiple instances in one window (columns or curves) to view multiple statistics data. - - {{:​statistics_dialog.png|Statistics dialog}} - - ==== Showed Statistical Properties ==== - By default some statistical properties are not shown. Click ''​Show''​ button to select which properties you want to calculate. - - ===== Statistical Functions in Column Formulas ===== - You can also calculate statistics on table columns using column statistics functions when entering column formula. See ''​Functions''​ tab in ''​Set Column Formula''​ dialog for column statistics functions description. These functions are also available in MagicPlot Student edition. - - ===== Computational Formulas ===== - Central moments are calculated as follows (see table). All sums are calculated using [[wp>​Compensated_summation|compensated summation]]. Central moments are calculated on second pass after Mean calculation. - ^  Property ​ ^  Formula ​ ^ - | //n// | The number of non-empty cells  | - | Mean | <​m>​nu_1 = 1/n sum{j}{}{a_j} ​ | - | [[wp>​Central moment|Central moments]] | <​m>​mu_k = 1/n sum{j}{}{(a_j − nu_1)^k}, ~ k = 2...4​ | - - MagicPlot uses the following formulas to calculate statistics: - ^  Property ​ ^  Formula ​ ^ - | Mean (expected value) | mu = nu_1​ | - | Variance | <​m>​sigma^2 = {n / {n − 1}} mu_2​ | - | Standard deviation | <​m>​sigma = sqrt{sigma^2}​ | - | Skewness | <​m>​gamma_1 = sqrt{n (n − 1)} / {n − 2} {mu_3} / {sigma^3}​ | - | Kurtosis | <​m>​gamma_2 = {n − 1} / {(n − 2)(n − 3)} ({(n + 1) {mu_4} / {sigma^4} − 3 (n − 1)})​ | - | Y Sum | s = sum{j}{}{a_j}​ | 