Descriptive Statistics Calculator

Complete descriptive statistics

A full descriptive statistics package boils a dataset down along three lines. There's position (n, min, max, mean, median, mode, Q1, Q3), dispersion (IQR = Q3 − Q1, variance, standard deviation, coefficient of variation CV = σ/μ), and shape, which covers skewness (negative leans to a left tail, positive to a right tail) and kurtosis (> 3 is leptokurtic with heavy tails, < 3 is platykurtic with light tails, both measured against the normal). It's the same idea behind df.describe() in pandas or summary() in R. The five-number summary (min, Q1, median, Q3, max) is what feeds the box-plot. Take [3, 5, 7, 7, 8, 9, 11, 12]: mean 7.75, median 7.5, Q1 = 6, Q3 = 10, IQR = 4.

Applications

This is the bread and butter of Exploratory Data Analysis (EDA), your first look at any dataset before you start modeling. It also shows up in sample planning, quality control (process capability), market research, dashboards and KPIs, and spotting outliers with the IQR rule (anything outside [Q1 − 1.5·IQR, Q3 + 1.5·IQR]).

FAQ

Skewness vs kurtosis? Skewness is about asymmetry: when the mean > median, you have positive skew. Kurtosis is about how heavy the tails are. Above 3 (leptokurtic) you get more outliers than a normal distribution would; below 3 (platykurtic) the tails are lighter. For reference, the normal sits at skew = 0 and kurtosis = 3.

What does the box-plot show? It draws the five-number summary. The box runs from Q1 to Q3 with the median marked inside, the whiskers reach out to 1.5·IQR, and anything past that gets flagged as an outlier. Handy when you want to line up distributions from different groups side by side.

Mean or median to summarize? The mean takes every data point into account, but a few outliers can throw it off; the median holds up better. With skewed data like income, prices, or response times, the median gives you a truer sense of the typical value.