A frequency diagram (sometimes called a histogram for grouped data) is used to display continuous data that has been grouped into class intervals. The key difference from a bar chart is that the bars touch each other — there are no gaps. This is because the data is continuous (there are no gaps in the actual values between intervals).
Frequency Diagram: continuous data → bars touch | Bar Chart: discrete/categorical data → bars have gaps
Example 1 — Identifying key features from the heights frequency diagram
Count the class intervals on the x-axis: 140–150, 150–160, 160–170, 170–180, 180–190. Each bar represents one interval.
Step 2
Check the y-axis (Frequency). Read the height of each bar against the y-axis scale.
Step 3
Total frequency = \(3 + 7 + 12 + 8 + 2 = 32\) students.
Step 4
The modal class is 160–170 (the tallest bar, frequency 12). Note: bars touch — no gaps.
Example 2 — Finding modal class and total frequency
A frequency diagram shows ages: 20–30 (5), 30–40 (15), 40–50 (20), 50–60 (10).
Step 1
Identify the tallest bar: 40–50 has frequency 20 — this is the modal class.
Step 2
Total frequency = \(5 + 15 + 20 + 10 = 50\) people surveyed.
Step 3
The modal class is written as an interval: 40–50, not as a single value.
Key rule: Bars in a frequency diagram always touch because the data is continuous — there are no gaps in values between, say, 150 cm and 160 cm. Leaving gaps would wrongly suggest some values are impossible.
✓ Quick Check 1 — Frequency diagrams and bars that touch
Question 1 of 10
Reading Frequency Diagrams
To read a frequency diagram accurately: find the class interval on the x-axis, then read across to the y-axis to get the frequency. You can also find the total frequency by adding all bar heights, and the modal class by identifying the tallest bar.
Example 1 — Reading values from the exercise frequency diagram
Use the diagram above (minutes of exercise per week: 0–60: 4, 60–120: 9, 120–180: 6, 180–240: 3).
Step 1
(a) Frequency for 60–120 minutes: Find the bar labelled 60–120 on the x-axis. Read across to the y-axis → frequency = 9.
Step 2
(b) Modal class: Identify the tallest bar. The 60–120 bar reaches frequency 9, the highest. Modal class = 60–120 minutes.
Step 3
(c) Total frequency: Add all bars: \(4 + 9 + 6 + 3 = \mathbf{22}\) people surveyed.
Example 2 — Interpreting what a frequency diagram tells us
The same exercise diagram. What fraction of people exercise between 60 and 120 minutes?
Step 1
Frequency for 60–120 = 9. Total frequency = 22.
Step 2
Fraction = \(\frac{9}{22}\). This cannot be simplified further.
Step 3
As a percentage: \(\frac{9}{22} \times 100 \approx 40.9\%\) of people exercise 60–120 minutes per week.
Modal class tip: The modal class is the class interval with the highest frequency — always write it as an interval (e.g. 60–120), not as a single value. You cannot find the exact mode from grouped data.
✓ Quick Check 2 — Reading frequency diagrams
Question 1 of 10
Drawing Frequency Diagrams — Step by Step
When drawing a frequency diagram from a table of data, follow these steps carefully. The key differences from a bar chart: bars touch (no gaps), x-axis is a continuous scale (not labels with spaces), and you must choose a uniform scale.
Real-life uses: Frequency diagrams appear in health reports (age distributions), business (salary bands), sport (race time distributions), and geography (rainfall totals per month).
Example 1 — Drawing a frequency diagram from a table
Data: Exam scores — 0–20 (2), 20–40 (5), 40–60 (14), 60–80 (11), 80–100 (3). Draw the frequency diagram.
Step 1
Draw a horizontal x-axis. Mark equal-width intervals: 0, 20, 40, 60, 80, 100. Label: "Score (%)".
Step 2
Draw a vertical y-axis. The highest frequency is 14. Choose a scale going up to at least 15. Label: "Frequency".
Step 3
Draw each bar to the correct height: bar from 0–20 reaches 2; bar from 20–40 reaches 5; bar from 40–60 reaches 14; bar from 60–80 reaches 11; bar from 80–100 reaches 3.
Step 4
Bars must touch. The left edge of the 20–40 bar is at the same point as the right edge of the 0–20 bar. No gaps.
Step 5
Add a title: "Exam Scores — Frequency Diagram". Modal class = 40–60 (highest bar).
Example 2 — Bar chart or frequency diagram?
A teacher records students' favourite subjects: Maths (10), English (8), Science (12), Art (6). Which type of chart should she use?
Step 1
Check the type of data: "Favourite subject" is categorical (discrete) — subjects are separate named categories, not a continuous measurement.
Step 2
Continuous data (heights, weights, times) → frequency diagram (touching bars). Categorical/discrete data (colours, subjects, names) → bar chart (gaps between bars).
Step 3
Answer: use a bar chart with gaps. A frequency diagram would be wrong here because there is no continuous scale on the x-axis.
Common mistake: Drawing gaps between bars in a frequency diagram. This is the single most common error in the exam. Frequency diagrams always have touching bars because the data is continuous.
✓ Quick Check 3 — Drawing frequency diagrams and real-life contexts
Question 1 of 10
Practice: Identify the Modal Class and Total Frequency
For each dataset, type the modal class (e.g. "30–40") and the total frequency. Then click Check All.
Leaving gaps between bars: Frequency diagrams show CONTINUOUS data (e.g. height, age). Bars must TOUCH — no gaps. Gaps imply no values in that range.
Confusing frequency diagrams with bar charts: Bar charts (categorical data) have gaps. Frequency diagrams (grouped continuous data) do not. The data type determines which to use.
Wrong class intervals on x-axis: Label the x-axis with the boundaries of each class (e.g. 0, 10, 20, 30) not the midpoints. Each bar spans from one boundary to the next.
Modal class vs mode: From a frequency diagram, you can identify the modal CLASS (the bar with the tallest height). You cannot identify a single modal value from grouped data.
Total frequency: Add all bar heights (frequencies) to find the total number of data items. The total is needed to find the mean and median.