Descriptive Statistics Explorer

An interactive guide to the fundamental metrics used to describe a dataset.

What Are Descriptive Statistics?

Descriptive statistics are the foundational tools we use to summarize and understand the main features of a dataset. They provide simple, quantitative summaries about the sample and the measures. They are the first step in any quantitative analysis, giving you a high-level "feel" for the data's characteristics before you dive into more complex modeling.

They are broadly divided into measures of **central tendency** (like mean, median, and mode) and measures of **variability or spread** (like standard deviation, variance, and kurtosis).

The Laboratory
Generate different data distributions and observe how the key statistics change in real-time. This is crucial for building an intuitive understanding of these concepts.
Mean

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Median

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Mode

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Std. Deviation

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Skewness

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Kurtosis (Excess)

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Interpreting the Metrics

Mean vs. Median

In a perfectly symmetrical (normal) distribution, the mean and median are the same. Notice how when you select a skewed distribution, the mean is "pulled" in the direction of the long tail, while the median is more robust and stays closer to the "center" of the main bulk of data. This is why the median is often a better measure of central tendency for skewed data like income or housing prices.

Standard Deviation

This measures the average distance of data points from the mean. A higher value indicates more spread or volatility.

Skewness

Measures the asymmetry of the distribution. A value near zero is symmetrical. A positive value indicates a "right-skewed" distribution (long tail to the right), and a negative value indicates a "left-skewed" distribution (long tail to the left).

Kurtosis

Measures the "tailedness" of the distribution. Excess kurtosis (what's shown here) is relative to a normal distribution. A positive value (Leptokurtic) means the distribution has fatter tails and a sharper peak, indicating more frequent extreme outliers than a normal distribution. A negative value (Platykurtic) means thinner tails and a flatter peak. Financial returns are famously leptokurtic.