Stats (Statistical Summary)

Syntax:
    stats {<ranges>} 'filename' {matrix | using N{:M}} {name 'prefix'} {{no}output}

This command prepares a statistical summary of the data in one or two columns of a file. The using specifier is interpreted in the same way as for plot commands. See plot (p. [*]) for details on the index (p. [*]), every (p. [*]), and using (p. [*]) directives. Data points are filtered against both xrange and yrange before analysis. See set xrange (p. [*]). The summary is printed to the screen by default. Output can be redirected to a file by prior use of the command set print, or suppressed altogether using the nooutput option.

In addition to printed output, the program stores the individual statistics into three sets of variables. The first set of variables reports how the data is laid out in the file: The array of column headers is generated only if option set datafile columnheaders is in effect.

STATS_records 72#72 total number 70#70 of in-range data records
STATS_outofrange 73#73 number of records filtered out by range limits
STATS_invalid 73#73 number of invalid/incomplete/missing records
STATS_blank 73#73 number of blank lines in the file
STATS_blocks 73#73 number of indexable blocks of data in the file
STATS_columns 73#73 number of data columns in the first row of data
STATS_column_header 73#73 array of strings holding column headers found

The second set reports properties of the in-range data from a single column. This column is treated as y. If the y axis is autoscaled then no range limits are applied. Otherwise only values in the range [ymin:ymax] are considered.

If two columns are analysed jointly by a single stats command, the suffix "_x" or "_y" is appended to each variable name. I.e. STATS_min_x is the minimum value found in the first column, while STATS_min_y is the minimum value found in the second column. In this case points are filtered by testing against both xrange and yrange.

STATS_min   74#74 minimum value of in-range data points
STATS_max   75#75 maximum value of in-range data points
STATS_index_min   76#76 index i for which data[i] == STATS_min
STATS_index_max   77#77 index i for which data[i] == STATS_max
STATS_mean 78#78 79#79 mean value of the in-range data points
STATS_stddev 80#80 81#81 population standard deviation of the in-range data
STATS_ssd 82#82 83#83 sample standard deviation of the in-range data
STATS_lo_quartile     value of the lower (1st) quartile boundary
STATS_median     median value
STATS_up_quartile     value of the upper (3rd) quartile boundary
STATS_sum   84#84 sum
STATS_sumsq   85#85 sum of squares
STATS_skewness   86#86 skewness of the in-range data points
STATS_kurtosis   87#87 kurtosis of the in-range data points
STATS_adev   88#88 mean absolute deviation of the in-range data
STATS_mean_err   89#89 standard error of the mean value
STATS_stddev_err   90#90 standard error of the standard deviation
STATS_skewness_err   91#91 standard error of the skewness
STATS_kurtosis_err   92#92 standard error of the kurtosis

The third set of variables is only relevant to analysis of two data columns.

STATS_correlation   sample correlation coefficient between x and y values
STATS_slope   A corresponding to a linear fit y = Ax + B
STATS_slope_err   uncertainty of A
STATS_intercept   B corresponding to a linear fit y = Ax + B
STATS_intercept_err   uncertainty of B
STATS_sumxy   sum of x*y
STATS_pos_min_y   x coordinate of a point with minimum y value
STATS_pos_max_y   x coordinate of a point with maximum y value

Keyword matrix indicates that the input consists of a matrix (see matrix (p. [*])); the usual statistics are generated by considering all matrix elements. The matrix dimensions are saved in variables STATS_size_x and STATS_size_y.

STATS_size_x   number of matrix columns
STATS_size_y   number of matrix rows

The index reported in STATS_index_xxx corresponds to the value of pseudo-column 0 ($0) in plot commands. I.e. the first point has index 0, the last point has index N-1.

Data values are sorted to find the median and quartile boundaries. If the total number of points N is odd, then the median value is taken as the value of data point (N+1)/2. If N is even, then the median is reported as the mean value of points N/2 and (N+2)/2. Equivalent treatment is used for the quartile boundaries.

For an example of using the stats command to annotate a subsequent plot, see stats.dem.

The stats command in this version of gnuplot can handle log-scaled data, but not the content of time/date fields (set xdata time or set ydata time). This restriction may be relaxed in a future version.


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