Data Interpretation • Topic 4 of 6

Histograms

A histogram groups numerical data into intervals (bins) and shows how many values fall in each bin with bars. Unlike a bar graph of categories, the bars sit on a continuous number scale. Questions ask for the total count (add all the frequencies), how many fall above or below a cut-off (add the relevant bins), or which interval is most common (the tallest bar). When a cut-off such as “at least 60” is given, include every bin from that point up. Be careful with interval boundaries and read the frequency, not the interval label, as the value you add.

A histogram with five adjacent bins of frequency 3, 7, 12, 8, 5Histogram04812020406080100

✅ Solved examples

1. Bins — 0–20:3, 20–40:7, 40–60:12, 60–80:8, 80–100:5. How many students total?
3 + 7 + 12 + 8 + 5 = 35.
2. Using the same data, how many scored at least 60?
60–80 and 80–100: 8 + 5 = 13.
3. Which interval is most common?
The tallest bar is 12, the 40–60 interval.
4. How many scored below 40?
0–20 and 20–40: 3 + 7 = 10.

✏️ Practice — try these, take hints as needed

1. Bins 0–10:4, 10–20:9, 20–30:6. What is the total frequency?
Add the bin heights.
4 + 9 + 6.
—
19.
2. Scores — 0–50:5, 50–100:12. How many scored at least 50?
Use the 50–100 bin.
12.
—
12.
3. Bins 0–20:6, 20–40:10, 40–60:4. Which interval is most common?
Tallest bar.
10.
—
20–40.
4. Bins 0–30:8, 30–60:5, 60–90:2. How many below 60?
Add the first two bins.
8 + 5.
—
13.
5. Bins 0–25:3, 25–50:7, 50–75:9, 75–100:6. Total?
Add all four.
3 + 7 + 9 + 6.
—
25.

📝 Topic test — 8 questions

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