Full descriptive statistics for a dataset: centre, spread, quartiles, skew and outliers.
Descriptive statistics summarise a dataset without assuming any distribution. The mean is the arithmetic average; the median is the middle value; the mode is the most frequent value (or no mode when all values are unique). Spread is captured by the range, variance and standard deviation. Quartiles divide the sorted data into four equal parts, and the IQR (Q3−Q1) is the middle 50 %. Tukey fences sit at Q1−1.5×IQR and Q3+1.5×IQR; any point outside them is flagged as an outlier. Skewness measures distributional asymmetry; excess kurtosis measures tail heaviness relative to a normal distribution.
Mean
Mean = (sum of all values) / n
Sample variance
Sample variance = Σ(xᵢ − x̄)² / (n−1)
Tukey fences
Lower fence = Q1 − 1.5·IQR; Upper fence = Q3 + 1.5·IQR
Choose sample (÷ n−1, Bessel's correction) when your data is a subset drawn from a larger population — the typical research scenario. Choose population (÷ n) only when your dataset contains every element of the population you care about, such as the grades of all 30 students in a specific class.
When every value appears exactly once, no value is more frequent than any other, so the dataset has no mode. Some textbook definitions force a mode in that case, but it conveys no useful information. This calculator honestly reports 'No mode' rather than inventing one.
This calculator uses Tukey fences: any data point below Q1−1.5×IQR or above Q3+1.5×IQR is classified as an outlier. This is the standard method used by box-and-whisker plots. For datasets with heavier tails you might apply a stricter 3×IQR rule, but 1.5 is the default.
Excess kurtosis compares the tail weight of your distribution to a normal distribution (which has excess kurtosis = 0). A positive value means heavier tails and more extreme values are likely; a negative value means lighter tails. It requires at least 4 data points to compute.