Math Playground
Data

Histograms

Bar charts for grouped numerical data — bins on the x-axis.

Take 1,000 people's heights and you can't list them. But sort them into bins — 150-155cm, 155-160cm, ... — and bar them up, and the shape of human height appears: a bell.

A histogram groups continuous data into intervals (bins) and shows how many values fall in each. It reveals the *shape* of a distribution — where it peaks, how it spreads, whether it's skewed.

Where you'll meet this

Quality control, exam-score analysis, image processing (brightness histograms), detecting skew before choosing mean vs median.

statisticsQAdata science
Edit the data — the chart follows
30-10710-201220-30930-40540-50250-60

Histogram vs bar graph

  • Bars touch (no gaps) — the variable is continuous.
  • X-axis is a number line of intervals, not category labels.
  • Bin width matters — too wide hides detail, too narrow looks like noise.
  • Area, not just height, can carry meaning if bins are unequal.
Your turn

A histogram of test scores has a tall bar at 90-100 and a long thin tail down to 30. Is it skewed? Which way?

Try it

Why might a histogram look bumpy with too many bins?

With narrow bins, random fluctuations dominate — you see 'noise' instead of the underlying shape. Wider bins smooth it out. There's an art to choosing bin width.

Watch out

Don't put gaps between histogram bars. Gaps mean 'separate categories' — but a histogram's intervals are continuous, so the bars must touch.

The Galton board above *is* a live histogram — each bin counts balls, and the shape that emerges is exactly what a histogram of a normal distribution looks like.

Recap
  • Histogram = distribution of continuous data in bins; bars touch.
  • Reveals shape: peak location, spread, skew.
  • Bin width is a real choice — too few hides detail, too many shows noise.