Histograms and Frequency Distributions

What is a histogram?

A histogram groups continuous data into bins (intervals) and shows the frequency (count) in each bin as a bar. Unlike bar charts, the bars touch because the x-axis is continuous.

Step-by-step

Given scores: 52, 55, 63, 67, 68, 71, 73, 75, 78, 79, 82, 84, 85, 88, 91, 93, 95

Step 1 — Define bins: [50,60), [60,70), [70,80), [80,90), [90,100]

Step 2 — Count frequencies:

• [50,60): 2 scores (52, 55)
• [60,70): 3 scores (63, 67, 68)
• [70,80): 5 scores (71, 73, 75, 78, 79)
• [80,90): 4 scores (82, 84, 85, 88)
• [90,100]: 3 scores (91, 93, 95)

Step 3 — Draw bars with heights proportional to frequency.

How bin width matters

• Too wide (e.g., one bin): all data in one bar — no shape information.
• Too narrow (e.g., width 1): too many bars — noise overwhelms pattern.
• Just right: reveals the shape (symmetric, skewed, bimodal, etc.).

Try it in the visualization

Adjust the bin width slider. Watch the same data produce dramatically different histogram shapes. The "right" bin width reveals the underlying distribution.