Grade by Grade
D. Data · Data Literacy and Probability

Choosing and Justifying the Best Graph

D1.3 A1About 45 minutes
Learning goals
  • I can describe what each type of graph is best at showing.
  • I can tell when a circle graph is a good choice and when it is not.
  • I can choose the best graph for a data set and justify my choice.

Words to know

justify
Give reasons that explain why your choice makes sense.
parts of a whole
Categories that together make up one complete group, with no overlaps, so the percentages add to 100%.
overlapping categories
Categories where one person can be in more than one, as in a "choose all that apply" question.

Remember from Grade 6

In Grade 6 you chose between bar graphs, multiple-bar graphs, stacked-bar graphs, histograms, broken-line graphs, line plots and stem-and-leaf plots, and you explained your choice. Now the circle graph joins the team.

The right tool for the job

You wouldn't use a hammer to cut paper. Each graph is a tool that is good at one kind of job. Before you choose, ask:

  1. What kind of data is it? Qualitative, discrete or continuous?
  2. What is my question? Am I comparing categories, showing parts of a whole, or showing change over time?
  3. Who will read the graph? What will be clearest for them?
GraphBest forExample
Circle graphParts of one whole; percentages that add to 100%; a few categoriesHow a class gets to school
Bar graphComparing categories (counts or percents), even when categories overlapNumber of students in each club
Multiple-bar graphComparing two or more groups across the same categoriesFavourite sport, Grade 4 vs Grade 7
Stacked-bar graphParts of a whole for several groups side by sideWay to school for each of 3 classes
HistogramNumber data (often continuous) grouped in equal intervalsHeights of 60 basil plants
Broken-line graphChange over timeNoon temperature each day in January
Line plot or stem-and-leaf plotA small set of numbers where you want to see every valueTest scores of 20 students
Choosing a graph

When is a circle graph a good choice?

A circle graph works when all of these are true:

  • The data is about one whole group.
  • Each person or thing is in exactly one category (no overlaps).
  • The percentages add to 100%.
  • There are only a few categories (about 6 or fewer).

A circle graph is not a good choice for change over time, for comparing exact amounts that are close together, or when people could choose more than one answer.

Worked example

Example 1: Which graph?

Choose the best graph for each data set, and give a reason.

(a) The temperature at noon each day for two weeks in January. (b) How Grade 7 students spend their allowance: the percent spent on food, entertainment, clothes and savings. (c) The heights of 60 basil plants in a science experiment.

  1. (a) The data changes over time. A broken-line graph shows the rises and falls from day to day.
  2. (b) The categories are parts of one whole (all the allowance money), and the percentages add to 100%. A circle graph shows how big each part is compared with the whole.
  3. (c) Height is continuous number data, and there are many values. A histogram with equal intervals shows the distribution.

(a) broken-line graph, (b) circle graph, (c) histogram.

Worked example

Example 2: When the answers overlap

Fifty students were asked, "Which of these do you do in winter? Choose all that apply." Skating 34, tobogganing 30, skiing 12, snowshoeing 9. Should you use a circle graph?

  1. Find the percentages: skating 34 ÷ 50 = 68%, tobogganing 60%, skiing 24%, snowshoeing 18%.
  2. Add them: 68 + 60 + 24 + 18 = 170%. That's more than 100%! Many students chose more than one activity.
  3. The categories overlap, so they are not parts of one whole. A circle graph would not make sense.
  4. A bar graph of percentages works well. Each bar shows the percent of students who do that activity.

No circle graph. Use a bar graph, because students could choose more than one answer, so the percentages add to more than 100%.

Winter Activities Students Do020406080Percent of students68Skating60Tobog.24Skiing18Snowsh.Source: 50 Grade 7 students; more than one answer allowed
Skating 68%, tobogganing 60%, skiing 24%, snowshoeing 18%. The bars add to more than 100% because students could choose more than one activity.
Worked example

Example 3: Two good choices, two different stories

The same travel data (bus 40%, walk 25%, car 20%, bike 10%, other 5%) can be shown as a circle graph or as a bar graph. Which should you use?

  1. A circle graph makes it easy to see each part compared with the whole: "The bus is a bit less than half."
  2. A bar graph makes it easy to compare the categories with each other and to read exact values from a scale: "Twice as many come by car as by bike."
  3. Choose the graph that best answers your question, then say why.

Both are reasonable. A good justification sounds like: "I chose a circle graph because the data shows parts of one whole and I want readers to see that almost half of students take the bus."

How 200 Grade 7 Students Get to School40%25%20%10%Bus 40%Walk 25%Car 20%Bike 10%Other 5%Source: Maple Ridge P.S. survey of 200 students
The travel data as a circle graph: you can see at a glance that the bus sector is a bit less than half the circle.

Justify with three parts

A strong justification names: (1) the type of data, (2) what you want the graph to show, and (3) why this graph shows it well. Example: "The data is continuous (time), I want to show how the times are spread out, and a histogram groups the times in equal intervals." When a classmate chooses a different graph, listen to their reasons. Two choices can both be good.

Just for fun

Using a circle graph to show change over time is like using a frying pan as a tennis racket. It's a perfectly good tool, just not for this job!

Hands-on activity

Graph detective

You need: a newspaper, a flyer, a magazine, or a news or sports website (look with a grown-up), and paper.

  1. Find three graphs. Look for at least one circle graph if you can.
  2. For each graph, write: the type of graph, the type of data, and the question the graph answers.
  3. Decide: Is this the best type of graph? Write one sentence to justify your answer.
  4. Pick one graph that could be better as a different type. Sketch the new graph.

Math talk: "Do the percentages in the circle graph add to 100%? Could anyone be in two categories?"

Your turn

1

Best graph for the number of hours of daylight in Thunder Bay on the first day of each month for a year?

2

Best graph for the percent of a family's garbage that is compost, recycling and trash?

3

Best graph for the arm spans of 40 students?

4

Best graph for favourite pizza topping for Grade 4 and Grade 7 students?

5

A survey asks, "Which streaming or TV services does your family use? Choose all that apply." Can you use a circle graph? Why?

6

Kai wants to show the exact quiz scores of the 12 students in his group. Which graph?

More practice: warm-up

1

Which graph is best for change over time?

2

Which graph is best for parts of one whole?

3

Which graph groups number data into equal intervals with touching bars?

4

In a circle graph, the percentages must add to what?

5

Which graph compares two groups across the same categories?

More practice: on your own

1

A survey has 12 categories of favourite snack, some with only 1%. Is a circle graph a good choice? What could you do?

2

Show how three classes (7A, 7B, 7C) get to school, so readers can compare the parts of each class. Which graph?

3

Two candidates got 51% and 49% of the votes. Why might a bar graph show this better than a circle graph?

4

Write a justification for using a histogram to show the time 50 students took to finish a puzzle.

5

Percents of students who play each sport: hockey 45%, soccer 52%, basketball 30%. Can these go in a circle graph?

Challenge

1

A town records how many people visited its library each month for a year, and also what percent of visitors were children, teens and adults. Which graph would you use for each part? Explain.

2

Describe a data set where a circle graph would be misleading even though the percentages add to 100%.

3

Riya's data: heights of 30 sunflowers measured each week for 8 weeks. She wants to show how one sunflower grew, and how tall all 30 were in week 8. Which two graphs should she use?

Check your understanding

Quiz

1.

Which data is best shown in a circle graph?

2.

Which graph is best for showing change over time?

3.

A "choose all that apply" survey has percentages that add to 140%. Which graph should you use?

4.

Which graph is best for the masses of 80 pumpkins grown in Ontario?

5.

What does a good justification for a graph include?

For parents and teachers

Big idea: Grade 7 students select the graph best suited to a data set, now including circle graphs, display it properly, and justify their choice (D1.3). The key test for a circle graph: one whole, no overlaps, percentages add to 100%, and not too many categories.

Common difficulties:

  • Using a circle graph for "choose all that apply" data (percentages over 100%).
  • Using a circle graph for change over time.
  • Justifying with "it looks nice" instead of naming the data type and purpose.

How to help: Look at graphs in the news or on sports sites together and ask, "Why did they choose this graph? Would another one be better?" Encourage your child to accept that two different graphs can both be good choices if the reasons are clear. This builds A1 skills: critical thinking, and respecting other people's ideas.