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A histogram is a graph that shows how data are distributed by grouping values into bins (intervals) and showing how many observations fall into each bin.

It’s perfect for visualizing:

• shape (skewed, symmetric, bimodal)
• spread
• clusters
• outliers

Think of it as stacking blocks into intervals to see where the data pile up.

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⭐ Key Features of a Histogram

• X‑axis: the bins (ranges of values)
• Y‑axis: frequency (count) or relative frequency (proportion)
• Bars touch because the data are continuous or ordered
• Bin width matters — too wide hides structure, too narrow creates noise

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⭐ Examples

Example 1: Test Scores

Suppose 30 students take a math test, and their scores range from 40 to 100.

If we choose bins of width 10 (40–49, 50–59, …):

Score Range	Frequency
40–49	2
50–59	5
60–69	8
70–79	9
80–89	4
90–100	2

A histogram would show:

• A peak around 70–79
• Fewer very low or very high scores
• A roughly bell‑shaped distribution

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Example 2: Heights of 100 People

Heights (in cm) might fall between 150 and 200.

If we use bins of width 5 cm:

• 150–155: 3 people
• 155–160: 7
• 160–165: 15
• 165–170: 22
• 170–175: 25
• 175–180: 18
• 180–185: 8
• 185–190: 2

The histogram would show:

• A strong peak around 170–175
• A symmetric, bell‑shaped pattern
• Very few extremely tall or short individuals

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Example 3: Daily Coffee Consumption

Survey 50 adults on how many cups of coffee they drink per day.

Cups per Day	Frequency
0	6
1	12
2	18
3	10
4	3
5+	1

A histogram would show:

• A right‑skewed distribution
• Most people drink 1–2 cups
• A long tail of heavy coffee drinkers

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⭐ Histogram vs. Bar Chart (Quick Reminder)

Feature	Histogram	Bar Chart
Data type	Numerical	Categorical
Bars touch?	Yes	No
X‑axis	Intervals	Categories
Shows	Distribution	Counts per category