Descriptive statistics calculator

A measure of central tendency answers where the data centre, and three are in common use. The mean is the arithmetic average and uses every value, which makes it the most informative summary for symmetric, interval data but also the most sensitive to extreme scores. The median is the middle value once the data are ordered, so it shrugs off outliers and is the honest centre for skewed measures such as income or response time. The mode is the most frequent value and is the only centre that makes sense for purely categorical data.

Choosing between them is really a choice about your data's shape and level of measurement. For a roughly symmetric distribution the mean and median almost coincide, so the mean is the natural report. When the distribution is skewed, the mean is pulled toward the long tail while the median stays put, and the gap between them is a quick informal read on the asymmetry. State the level of measurement before you pick a centre; the wider question of how variable type drives every analysis choice sits in our guide to independent and dependent variables.

A centre is only half the story; dispersion tells you how tightly the values cluster around it. The range is the simplest measure, the largest value minus the smallest, but it depends entirely on the two most extreme points and ignores everything between them. The variance is the average squared deviation from the mean, which uses every value but lives in squared units that are awkward to read. Taking its square root returns the standard deviation, the everyday measure of spread, expressed in the same units as the original data.

The standard deviation is the figure to report beside the mean, because together they describe a distribution compactly: in a roughly normal variable about 68 percent of cases fall within one standard deviation of the mean and about 95 percent within two. A small value means the data huddle near the centre while a large one means they are widely scattered. To compare spread across variables measured on different scales, divide the standard deviation by the mean for a coefficient of variation, and feed the standard deviation into the calculator for Cohen's d and its relatives when you need a standardised difference between groups.

Descriptive statistics describe the sample in front of you, nothing more. They condense a column of numbers into a centre, a spread, and a shape so a reader can grasp the data at a glance, but they make no claim about anyone you did not measure. The mean, standard deviation, and the frequency table that open a results chapter are all descriptive: faithful summaries of the people or cases actually in the study.

Inferential statistics take the riskier step of generalising from the sample to the wider population. A confidence interval, a t-test, or a p-value all try to say something about cases you never observed, which is why they rely on probability and on assumptions about how the sample was drawn. Most dissertations report both in sequence: descriptives to introduce the data, then inference to test the hypotheses. Our explainer on where description ends and inference begins draws the line in detail, and the test selector tool helps you pick the inferential test that fits your design.

Beyond centre and spread, two figures describe the shape of a distribution. Skewness measures asymmetry: a positive value signals a long right tail of high scores, a negative value a long left tail, and zero a symmetric distribution. Kurtosis measures how heavy the tails are relative to a normal curve; this tool reports excess kurtosis, so a normal distribution reads zero rather than three, and a positive value warns of heavier tails and more frequent extreme scores than normal.

Shape matters because so many tests assume approximate normality. A common working rule treats skewness and excess kurtosis between -1 and +1 as close enough to normal for most parametric analyses, with some authors stretching to -2 and +2. When the figures drift well beyond that, consider transforming the variable or switching to a rank-based method, a fork covered in our note on when to switch to a nonparametric test. For a formal verdict rather than a rule of thumb, pair these numbers with a dedicated test for normality such as Shapiro-Wilk.

When you summarise more than one or two variables, a table beats a wall of sentences. The conventional layout gives one row per variable and columns for the sample size, the mean, the standard deviation, and often the minimum and maximum, with skewness and kurtosis added when normality is in question. In APA style the mean and standard deviation usually travel together, commonly written as M = 24.6, SD = 4.1, with values rounded to two decimal places and aligned on the decimal point for readability.

Keep categorical and continuous variables in separate tables, since counts and percentages do not belong in the same columns as means. Give the table a clear numbered caption, report the unit of measurement, and write a short paragraph above it that points to the patterns worth noticing rather than restating every cell. For the precise formatting of decimals, italics, and table notes, follow our guide to formatting statistics the APA way, and format the finished sentences automatically rather than assembling them by hand.