# Summary statistics

This function computes a number of basic descriptive statistics for one or more samples of univariate data. The samples can be given in one or more separate columns or with a single data column and a group column. Each sample must have at least 3 values. The columns can have different numbers of values.

The following numbers are shown for each sample (for equations see the Past manual):

**N**

The number of values n in the sample

**Min**

The minimum value

**Max**

The maximum value

**Mean**

The estimate of the mean

**Std. error**

The standard error of the estimate of the mean

**Variance**

The sample variance

**Stand. dev.**

The sample standard deviation

**Median**

The median of the sample. For n odd, the given value such that there are equally many values above and below. For n even, the average of the two central values.

**25 prcntil**

The 25th percentile, i.e. the given value such that 25% of the sample is below, 75% above. The “interpolation” method is used (see Percentile plot).

**75 prcntil**

The 75th percentile, i.e. the given value such that 75% of the sample is below, 25% above. The “interpolation” method is used (see Percentile plot).

**Skewness**

The sample skewness, zero for a normal distribution, positive for a tail to the right. Note there are several versions of this around – Past uses the same equation as SPSS and Excel. Slightly different results may occur using other programs, especially for small sample sizes.

**Kurtosis**

The sample kurtosis, zero for a normal distribution. Again Past uses the same equation as SPSS and Excel.

**Geom. mean**

The geometric mean. Logarithms are used internally.

**Coeff.var**

Coefficient of variation, or ratio of standard deviation to the mean, in percent.

#### Bootstrapping

Selecting bootstrapping will compute lower and upper limits for 95% confidence intervals, using the specified number of bootstrap replicates. Confidence intervals for the min and max values are not given, because bootstrapping is known to not work well for these statistics. Three different bootstrap methods are available, see the Past manual for details.

Missing data: Supported by deletion.