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D1.3 · Choose and label histograms or broken-line graphs
Learn to choose and label histograms or broken-line graphs through clear examples and targeted practice.
Ontario Grade 6 Mathematics
Data
Match the graph to the question and data
Different graphs answer different questions. A histogram groups numerical measurements into consecutive intervals and shows how many values fall into each interval. Its bars touch because the intervals meet. A broken-line graph instead connects values observed in time order to show change over time. The sample data here are explicitly hypothetical; they do not describe real students or a school. We will choose a histogram to summarize a set of reading times.
What you will learn
- Choose a graph based on data type and question.
- Label histogram intervals and frequency.
- Explain when a broken-line graph would be more suitable.
Group measured values
Suppose hypothetical reading times in minutes fall into 0–9, 10–19, 20–29, and 30–39 minute intervals. Imagine frequencies of 2, 5, 4, and 1. The intervals are consecutive and do not overlap, so each reading time belongs to exactly one bin. Their frequencies total 12 observations.
Draw a faithful histogram
Place the time intervals in numerical order on the horizontal axis and the number of observations on the vertical axis. Bars for neighbouring intervals touch. A histogram groups observations; it does not show that one particular student read for exactly 15 minutes. Put a clear title and source with the graph.
Contrast a time-series graph
If the same class recorded its average reading time each day from Monday through Friday, a broken-line graph could show how the average changed across those ordered days. Connecting histogram bar tops would be misleading: 0–9, 10–19, and 20–29 are ranges of values, not consecutive dates.
Worked example
Reading-time distribution
A hypothetical set has 2 readings in 0–9 minutes, 5 in 10–19, 4 in 20–29, and 1 in 30–39. Which graph summarizes the distribution?
Touching bars represent consecutive minute ranges; heights 2, 5, 4, and 1 sum to 12 observations. These values are invented for practice.
- Identify dataReading time is numerical and grouped into adjoining ranges.
- Choose graphA histogram displays the frequency in each range.
- Check totals2 + 5 + 4 + 1 = 12 hypothetical observations.
Answer: Use a histogram with consecutive time bins and frequency on the vertical axis.
Check: The 10–19 minute bar is highest at five readings.
Common mistakes and how to avoid them
Using a broken-line graph for grouped intervals.
Correction: Use a broken-line graph for ordered observations over time, not for a frequency distribution.
Lesson summary
- Histogram bars touch for consecutive numerical ranges.
- Broken-line graphs display changes across ordered time points.
- Always identify whether data are supplied, observed, or hypothetical.
Check your understanding
Question 1
Which graph best shows a temperature recorded each day for one week?
- Broken-line graph
- Histogram of age groups
- Pictograph without dates
- Unlabelled bar chart
Show answer and explanation
Broken-line graph
Daily temperature is an ordered time series, so a broken-line graph shows its change.
Key terms
- Frequency
- The number of observations in an interval.
- Histogram
- A graph of frequencies in consecutive numerical intervals.
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Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation D1.3. It is a study resource, not an official curriculum publication.
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