Descriptive Statistics and Distributions

Measures of Central Tendency

The mean, median, and mode each answer "what's typical here?" in a different way, and picking the wrong one can quietly mislead an audience. The mean (average) is sensitive to extreme values — a handful of very high earners will pull average income well above what a typical person earns. The median (the middle value when sorted) is more resistant to extremes and better represents the "typical" case in a skewed distribution, like income, home prices, or response times. The mode (the most frequent value) is most useful for categorical data or when you specifically care about the most common outcome rather than a central average.

A practical habit: whenever you report a mean, glance at the median too. If they're close, the distribution is roughly symmetric and the mean is a fair summary. If they're far apart, the distribution is skewed, and reporting only the mean risks giving a distorted impression of what's typical.

Measures of Spread

Central tendency alone hides how much variation exists. Two datasets can have the same average and look completely different. Range (max minus min) is simple but overly sensitive to a single extreme value. Standard deviation measures how far values typically sit from the mean, and is most meaningful when the distribution is roughly normal. Interquartile range (IQR) — the range covering the middle 50% of the data — is more robust to outliers and pairs naturally with the median as a spread measure for skewed data.

Spread matters for decisions, not just description. A metric with high variance is much less predictable than one with the same average but low variance, and that difference should shape how confidently you act on it.

Understanding Distribution Shape

A distribution's shape tells you things a single number can't. A normal (bell-shaped) distribution is symmetric around the mean, and many statistical techniques assume something close to this shape. A right-skewed distribution has a long tail toward high values — income and home prices are classic examples — and its mean sits above its median. A left-skewed distribution has a long tail toward low values, with the mean sitting below the median. A bimodal distribution has two peaks, which usually signals that you're looking at two distinct groups blended into one column — for example, transaction amounts from both individual and bulk business customers mixed in the same field.

Kurtosis describes how heavy a distribution's tails are compared to a normal distribution — a high-kurtosis distribution produces more extreme outliers than you'd expect, which matters for risk-sensitive metrics like transaction fraud or server latency.

Reading a Histogram and Box Plot

A histogram buckets values into ranges (bins) and shows how many observations fall into each, making skew, multiple peaks, and gaps immediately visible in a way raw numbers can't. Bin width matters: too few bins hide structure, too many bins turn the shape into noise, so it's worth trying a couple of bin counts before settling on one.

A box plot compresses a distribution into five numbers — minimum, first quartile, median, third quartile, and maximum — with points beyond a calculated threshold shown individually as likely outliers. Box plots are especially useful for comparing the same metric across several categories side by side, something a single histogram can't do well.

Practical Review Checklist

Before moving on, confirm that you can:

• Explain when median is a better summary than mean, and why
• Compare range, standard deviation, and IQR as measures of spread
• Identify a right-skewed, left-skewed, and bimodal distribution from a histogram
• Read the five key values represented in a box plot
• Explain why a bimodal distribution might signal two blended groups

Conclusion

Summary statistics and distribution shape are the foundation everything else in EDA builds on. Get comfortable reading them quickly, and you'll catch data problems and real patterns long before you open a charting tool.