Grade by Grade
D. Data · Data and Probability

Choosing the Best Graph

D1.3 A1About 45 minutes
Learning goals
  • I can tell what each kind of graph or table is good for.
  • I can choose the best graph for a set of data and justify my choice.
  • I can choose a scale that starts at 0, has equal steps and fits the data.
  • I can check a graph for a title, labels, a scale, a legend if needed, and a source.

Words to know

pictograph
A graph that uses pictures to show data. A key tells how many each picture stands for.
bar graph
A graph that uses bars to show one set of data.
multiple-bar graph
A graph with bars side by side to compare two or more sets of data.
stem-and-leaf plot
A display that organizes number data by tens (stems) and ones (leaves).
justify
Give reasons that explain why your choice makes sense.

Remember

In Grade 3 you made pictographs where one picture stood for many, and bar graphs with scales of 2s, 5s and 10s. In this unit you added stem-and-leaf plots and multiple-bar graphs. Now you have a whole toolbox!

The right tool for the job

You wouldn't use a hammer to cut paper. You would choose scissors, because they are the right tool for the job. Graphs are tools too. Each kind of graph is best at showing certain kinds of data. A good data detective chooses the graph that makes the data easiest to understand, and can justify (explain) the choice.

DisplayBest forExample
Frequency tableOrganizing counts and showing exact numbersTallies of favourite snacks turned into numbers
PictographOne set of category data with a few categories; eye-catchingBooks read by four friends, 🍎 = 5 books
Bar graphOne set of data in categories; easy to compare barsOur class's favourite season
Multiple-bar graphTwo or more sets of data with the same categoriesFavourite season of kids and of grown-ups
Stem-and-leaf plotMany two-digit number values; shows every value in orderJumping jacks done by 25 students
Each display has a job it does best.

Ask yourself three questions

  1. Are my data categories (qualitative) or number values (quantitative)?
  2. Do I have one set of data, or two or more sets to compare?
  3. Are there lots of different number values? Then a stem-and-leaf plot keeps every value and puts them in order.
Worked example

Example 1: Choose a display

Which display is best?

  1. The heights, in centimetres, of 20 bean plants (from 18 cm to 45 cm).
  2. The favourite lunches of the Grade 4 class and the Grade 5 class.
  3. The number of cans each of 4 classes brought to the food drive: 35, 50, 20, 45.
  1. 1: Many different two-digit numbers. A stem-and-leaf plot shows every height in order, and where most heights are.
  2. 2: Two sets of category data with the same lunches. A multiple-bar graph puts the classes side by side.
  3. 3: One set, four categories (the classes). A bar graph works well. A pictograph with a key of 5 cans would also work (7, 10, 4 and 9 pictures).

1 stem-and-leaf plot, 2 multiple-bar graph, 3 bar graph (or a pictograph with a key).

Choosing a good scale

For a bar graph or a multiple-bar graph:

  • The scale starts at 0.
  • It goes up by equal steps (the interval).
  • Look at the largest value. Choose an interval so you have about 5 to 10 steps.
  • The top of the scale should be at or a little above the largest value.
Worked example

Example 2: Choose a scale

The food drive data is 35, 50, 20 and 45 cans. Which interval should the scale use?

  1. Counting by 1s would need 50 steps. Far too many lines!
  2. Counting by 100s would give just one step (0, 100). The bars would be tiny and hard to compare.
  3. Counting by 5s from 0 to 50 gives 10 steps. Every value lands on a line.
  4. Counting by 10s from 0 to 50 gives 5 steps. 35 and 45 land halfway between lines, which is easy to read too.

Count by 5s (or by 10s) from 0 to 50.

What's wrong with this graph?

Look at this graph closely before you read on.

0251020FoxOwlBearMoose
A graph with problems. The scale reads 0, 2, 5, 10, 20, but the lines are the same distance apart.
Worked example

Example 3: Find and fix the problems

What is wrong with the graph above? How can we fix it?

  1. There is no title. We don't know what the graph is about.
  2. There are no axis labels and no source.
  3. The scale is not equal. From 0 to 2 is 2, from 2 to 5 is 3, from 5 to 10 is 5, and from 10 to 20 is 10. Because of this, the Moose bar (20) looks only a little taller than the Owl bar (10), even though 20 is double 10.
  4. Fix: count by 5s from 0 to 25, and add a title, labels and a source.

See the fixed graph below. Now the Moose bar is twice as tall as the Owl bar, as it should be.

Votes for Our Class Mascot0510152025FoxOwlBearMooseMascotNumber of votesSource: class vote, September 2026
The fixed graph: votes for our class mascot. Fox 5, Owl 10, Bear 2, Moose 20.
Worked example

Example 4: Justify a choice

Nia surveyed kids and grown-ups about their favourite season. Which graph should she use? Justify the choice.

  1. The data are categories (seasons), so a stem-and-leaf plot doesn't fit.
  2. There are two sets (kids and grown-ups) with the same categories.
  3. A multiple-bar graph shows the two sets side by side, with a legend.

"I chose a multiple-bar graph because I have two groups to compare, and bars side by side make it easy to see where kids and grown-ups agree and disagree."

Math talk

Sometimes more than one choice is good. A bar graph and a pictograph can both show the food drive data. What matters is your reason. Use the frame: "I chose ___ because ___." Listen to a classmate's reason too. They might notice something you didn't.

Just for fun

Choosing the wrong graph is like wearing swim flippers to go skating. Sure, you have something on your feet... but it won't help you much!

Hands-on activity

One data set, two ways

You need: your kids versus grown-ups survey (or any small survey), paper, a ruler and pencil crayons.

  1. Show your data as a pictograph with a key. Choose a picture that's quick to draw.
  2. Show the same data as a multiple-bar graph (or a bar graph for just one group).
  3. Ask a family member: "Which graph makes it easier to compare the kids and the grown-ups?" and "Which one is more fun to look at?"
  4. Write a sentence to justify which display you think is best: "I think the ___ is best because ___."

Your turn

1

The number of minutes each of 25 students read last night (from 5 to 60 minutes). Which display is best?

2

The favourite recess games of a Grade 2 class and a Grade 4 class. Which graph is best?

3

The favourite toque colour of the students in your class. Which graph could you use?

4

The largest value in your data is 18. Suggest a scale.

5

The largest value is 90. Suggest a scale.

6

Which display lists the exact count for each answer before you make a graph?

7

A scale reads 0, 5, 10, 20, 25. What is wrong?

More practice: warm-up

1

Which graph uses a legend to compare two or more sets of data?

2

Which display shows every value of two-digit data in order?

3

Which graph uses pictures and a key?

4

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

5

Name three parts every graph needs.

More practice: on your own

1

Mia counted the number of cars that passed her house each day for 30 days. The counts were between 12 and 58. Which display is best? Why?

2

The food drive data is 35, 50, 20 and 45 cans. Why would a pictograph with a key of 1 can be a poor choice?

3

The largest value in a data set is 240. Suggest a scale.

4

Jay made two separate bar graphs, one for kids and one for grown-ups, to compare their favourite seasons. Suggest a better choice and justify it.

5

A bar graph's scale goes from 0 to 1000 by 100s, but the values are 4, 7 and 9. What is the problem?

Challenge

1

The gym teacher recorded how many laps each of 24 students ran. She wants to see the smallest and largest number of laps and where most of the values are. Should she use a pictograph or a stem-and-leaf plot? Justify.

2

A graph shows Fox 22 votes and Owl 24 votes, but its scale starts at 20. Why might this graph trick a reader?

3

You surveyed Grades 3, 4 and 5 about their favourite lunch. The biggest frequency is 28. Choose a graph and a scale, and justify.

Check your understanding

Quiz

1.

Which display is best for the heights in centimetres of 30 sunflowers?

2.

Which is best for comparing the favourite sports of Grade 4 and Grade 6?

3.

Which scale is set up correctly?

4.

The largest value is 35. Which interval gives a good number of steps?

5.

What does it mean to justify your choice of graph?

6.

A graph has bars, a scale and labels. What is it still missing if it has no words at the top?

For parents and teachers

What this lesson teaches: choosing among frequency tables, pictographs, bar graphs, multiple-bar graphs and stem-and-leaf plots; choosing a scale that starts at 0 with equal steps; including titles, labels, legends and sources; and justifying the choice (D1.3). Explaining reasons and listening to others' reasons (A1) is built in.

How to help at home:

  • When you see a graph in the news or a flyer, ask: "Why do you think they chose this kind of graph? Is the scale fair?"
  • Ask "I chose ___ because ___" questions about everyday choices so your child gets used to giving reasons.

Common difficulties:

  • Choosing a pictograph or bar graph for many different number values. A stem-and-leaf plot keeps every value.
  • Uneven scales, or scales that don't start at 0, which can make differences look bigger or smaller than they are.
  • Picking intervals that are much too small or much too big for the data.
  • Thinking there is only one right graph. Reward good reasons.