Grade by Grade
D. Data · Data and Probability

Choosing and Making the Best Graph

D1.3 A1About 45 minutes
Learning goals
  • I can choose the best table or graph for a set of data, including stacked-bar graphs.
  • I can justify my choice of graph.
  • I can choose a fair scale that starts at 0 and counts by equal steps.
  • I can include a title, labels, a legend, a scale and a source.

Words to know

justify
Give a reason that explains your choice.
interval
The equal step between numbers on a scale, like counting by 5s.
source
Where the data came from.
axis
One of the two lines that frame a graph. One axis shows the categories and the other shows the scale.

Remember from Grade 4

You chose among frequency tables, pictographs, bar graphs, multiple-bar graphs and stem-and-leaf plots, and justified your choice with "I chose ___ because ___." This year your toolbox gets two more tools: the relative-frequency table and the stacked-bar graph.

The data toolbox

A carpenter picks the right tool for each job. A data detective picks the display that makes the data easiest to understand.

DisplayBest for
Frequency tableOrganizing counts and showing exact numbers
Relative-frequency tableShowing what share of the whole each category is; comparing groups of different sizes
PictographOne set of category data with a few categories; eye-catching
Bar graphOne set of category data; easy to compare categories
Multiple-bar graphTwo or more sets of data with the same categories; comparing one category across groups
Stacked-bar graphShowing the total for each group and the parts that make it up
Stacked-bar graph of relative frequenciesComparing the shares of groups of different sizes
Stem-and-leaf plotMany different number values (like heights or scores); shows every value in order
Each display has a job it does best.

Questions to ask yourself

  1. Is my data categories (like favourite sport) or number values (like heights)? Many different number values → stem-and-leaf plot.
  2. Do I have one set of data or two or more sets?
  3. Do I want to show totals and parts? → stacked-bar graph.
  4. Are my groups different sizes, and do I want to compare shares? → relative frequencies.

Sometimes two choices are both good. What matters is your reason.

Ask yourself...Then choose...Many different number values?yesStem-and-leaf plotTotals AND their parts for each group?yesStacked-bar graphShares of groups of different sizes?yesRelative frequenciesOne category across two or more groups?yesMultiple-bar graphJust one set of category data?yesBar graph or pictograph
Match your question to a display. Read down the left until you find the one that fits your data, then follow the arrow. If two fit, choose one and give your reason.

Choosing a fair scale

  • Start at 0.
  • Count up by equal steps (the interval), like 2s, 5s, 10s or 25s.
  • For a stacked-bar graph, look at the largest total, not the largest part.
  • Aim for about 5 to 10 steps, with the top of the scale at or a little above the largest value.
Worked example

Example 1: Make a stacked-bar graph

The Grade 5 classes recorded the books they borrowed from the library each week.

  • Week 1: fiction 18, non-fiction 12, graphic novels 10
  • Week 2: fiction 15, non-fiction 14, graphic novels 14
  • Week 3: fiction 20, non-fiction 10, graphic novels 17

The librarian wants to see how many books were borrowed each week and what kinds. Choose a graph, choose a scale, and draw it.

  1. Choose the graph. The librarian wants totals and parts, so a stacked-bar graph is best.
  2. Find the totals. Week 1: 18 + 12 + 10 = 40. Week 2: 15 + 14 + 14 = 43. Week 3: 20 + 10 + 17 = 47.
  3. Choose a scale. The largest total is 47. Counting by 5s up to 50 gives 10 steps. ✓
  4. Draw each bar from the bottom up, with the same order in every bar: fiction, then non-fiction, then graphic novels. Week 1: fiction 0 to 18, non-fiction 18 to 30, graphic 30 to 40.
  5. Finish it. Add a title, axis labels, a legend and a source.

See the finished graph below. Justification: I chose a stacked-bar graph because it shows the total books each week and how many of each kind.

Books Borrowed by Grade 5FictionNon-fictionGraphic05101520253035404550181210Week 1151414Week 2201017Week 3WeekNumber of booksSource: school library records, February 2026
The finished stacked-bar graph. Each bar goes fiction (green), non-fiction (yellow), graphic novels (blue), from the bottom up. Week 1 total 40, Week 2 total 43, Week 3 total 47. The scale counts by 5s.
Worked example

Example 2: Choose and justify

Which display would you choose for each data set?

  1. The arm spans, in centimetres, of 28 students.
  2. The favourite season of Grade 2 students and of Grade 5 students, to see which season each grade likes most.
  3. How students in a class of 18 and a class of 30 get to school, to compare what share of each class walks.
  1. Arm spans are many different number values. → Stem-and-leaf plot. It keeps every value in order.
  2. Two sets of category data with the same categories. → Multiple-bar graph. The bars for each season stand side by side, so they are easy to compare.
  3. Two classes of different sizes, comparing shares. → Relative-frequency table or a stacked-bar graph of relative frequencies, where each bar is 1 whole class.
  1. Stem-and-leaf plot. 2. Multiple-bar graph. 3. Relative frequencies, shown in a table or a stacked-bar graph where every bar is 1 whole.

Giving helpful feedback

When you check a classmate's graph, start with something they did well, then ask a question instead of just saying it's wrong: "I like your legend. How did you choose your scale?" When you get feedback, take a breath and see it as a way to make your graph better.

Just for fun

Funny but true: a stem-and-leaf plot has no real stems and no real leaves. You will never need to water one, and it won't drop leaves on the floor in the fall!

Hands-on activity

Graph makeover

You need: grid paper (or lined paper), a ruler, and coloured pencils.

  1. Ask 10 to 15 people at home or on a video call two questions: "What's your favourite winter treat: hot chocolate, maple taffy or soup?" and "Are you under 18 or 18 and older?"
  2. Decide: do you want to show each age group's total and parts, or compare one treat across the age groups? Choose a stacked-bar graph or a multiple-bar graph.
  3. Choose a scale that starts at 0 with equal steps.
  4. Draw the graph with a title, axis labels, a legend and a source.
  5. Write your justification: "I chose ___ because ___." Ask your grown-up to give you one star (something good) and one wish (something to improve).

Your turn

1

What display would you choose for the favourite pizza topping of 25 students? Why?

2

What display would you choose for the heights in centimetres of 30 students? Why?

3

What would you choose to show how students in three classes get to school (walk, bus, car), showing each class's total and parts?

4

What would you choose to compare the share of students who walk in a class of 18 and a class of 30?

5

The largest value in a bar graph is 63. Choose a scale.

6

A stacked-bar graph has no legend. Why is that a problem?

More practice: warm-up

1

What number should a bar graph's scale start at?

2

What does the title of a graph tell you?

3

What does the source tell you?

4

Which graph shows totals and parts in one bar?

5

A scale goes 0, 10, 20, 30, 40. What is the interval?

More practice: on your own

1

The largest value is 18. Choose a scale.

2

The largest value is 240. Choose a scale, and explain why counting by 1s is a bad idea.

3

A stacked-bar graph has bars with totals 26, 34 and 41. The biggest part is 20. What should the top of the scale be?

4

Jade made a pictograph of the arm spans of 30 students. Suggest a better choice and explain.

5

Write a justification for using a multiple-bar graph to compare the favourite sports of Grade 3 and Grade 5 students.

Challenge

1

Room 2: walk 8, bus 12, car 4 (24 students). Room 3: walk 15, bus 10, car 5 (30 students). Which graph would you use to answer each question? (a) Which room has more students who take the bus? (b) Which room has the greater share of walkers?

2

A bar graph's scale says 0, 5, 10, 20, 40, but the lines are the same distance apart. What's wrong? How would you fix it?

3

Describe a data set where a stacked-bar graph is a better choice than a multiple-bar graph, and explain why.

Check your understanding

Quiz

1.

Which display is best for many different number values, like the heights of 30 students?

2.

Which display is best for showing each class's total and the parts that make it up?

3.

Two classes are different sizes. You want to compare the share of each class that skis. What should you use?

4.

The largest total in a stacked-bar graph is 47. Which scale is best?

5.

Which is not needed on a stacked-bar graph?

6.

Which sentence is a justification?

For parents and teachers

What this lesson teaches: choosing the most suitable display, including stacked-bar graphs and relative-frequency tables, choosing a fair scale, including all graph parts (title, labels, legend, scale, source), and justifying the choice (D1.3). Giving and receiving feedback kindly (A1) is built in.

How to help at home:

  • Use the "star and a wish" approach when your child shows you a graph: one thing that works well, one thing to improve.
  • Ask "Why did you choose that kind of graph?" and accept any well-reasoned answer.

Common difficulties:

  • Choosing a scale from the largest part instead of the largest total in a stacked-bar graph.
  • Unequal steps or scales that don't start at 0.
  • Forgetting the legend or the source.
  • Giving a description ("it has bars") instead of a reason.