Grade by Grade
D. Data · Data Literacy and Probability

Choosing and Justifying the Best Graph

D1.3 A1About 45 minutes
Learning goals
  • I can choose the type of graph that best fits a set of data.
  • I can give a reason for my choice of graph.
  • I can include a title, labels, an appropriate scale and a source on every graph.
  • I can give and use helpful feedback on a graph.

Words to know

source
Where the data came from, such as "survey of Room 6, January".
scale
The numbers on an axis, going up in equal steps.
justify
To give a reason that explains why your choice makes sense.
line plot
A number line with an X or dot above it for each data value.

Remember

You have made many kinds of graphs: line plots and bar graphs in the early grades, stem-and-leaf plots and multiple-bar graphs in Grade 4, stacked-bar graphs in Grade 5, and now histograms and broken-line graphs. The skill now is choosing the right one for the job.

Every graph has a job

Before choosing, ask two questions:

  1. What kind of data is it? Qualitative (categories), discrete (counted) or continuous (measured)?
  2. What do I want to show? A comparison? How the data is spread out? A change over time? Parts of a whole?
GraphBest jobExample
Bar graphCompare categoriesFavourite winter activity
Multiple-bar graphCompare categories for two or more groups, side by sideFavourite activity, boys and girls
Stacked-bar graphShow totals and the parts that make them upBooks borrowed each day, split by type
Line plotShow every value of a small set of numbersNumber of pets of 15 students
Stem-and-leaf plotShow every value of a set of numbers in order; find the median and modeQuiz scores out of 50
HistogramShow how lots of numerical data is spread out, in intervalsHeights of 60 students
Broken-line graphShow how continuous data changes over timeTemperature every hour
Choosing a graph: what kind of data, and what job?
Four graphs, four different jobsBar graphcomparecategoriesHistogramspread of lotsof numbersBroken-linechange overtimeStem-and-leafevery value,in orderStemLeaf25 830 2 2 741 653
Bar graph bars have spaces (categories). Histogram bars touch (a number line). A broken-line graph follows time. A stem-and-leaf plot keeps every value (here 25, 28, 30, 32, 32, 37, 41, 46, 53).

Every graph needs...

  • A title that tells what the graph is about.
  • Axis labels, with units (cm, minutes, °C) where needed.
  • A scale that starts at 0 for bar graphs and histograms, goes up by equal steps, and fits the largest value without wasting space. About 5 to 10 steps is usually easy to read.
  • A legend if there is more than one colour or pattern.
  • A source, so readers know where the data came from and whether to trust it.
Favourite Winter Activity in Room 602468101214Number of students9Skating12Sledding4Skiing5SnowshoeActivitySource: survey of Room 6, January
A complete bar graph: title, axis labels, a scale from 0 to 14 by 2s that fits the tallest bar (12), and spaces between the bars because each is a category. Skating 9, Sledding 12, Skiing 4, Snowshoeing 5. The source is printed at the bottom.
Worked example

Example 1: Choose and justify

Choose the best graph for each, and justify your choice.

  1. The temperature in a greenhouse every hour from 8 a.m. to 6 p.m.
  2. The masses of 50 pumpkins at a farm.
  3. The favourite type of book of Grade 6 students and of Grade 7 students.
  4. The scores of 18 students on a quiz out of 40.
  1. 1. Temperature is continuous and changes over time. Broken-line graph.
  2. 2. Mass is continuous, and there are lots of values, almost all different. Group them in intervals: histogram.
  3. 3. Type of book is qualitative, and there are two groups to compare: multiple-bar graph.
  4. 4. A small set of numbers where we want to see every score in order: stem-and-leaf plot (or a line plot).
  1. Broken-line graph. 2. Histogram. 3. Multiple-bar graph. 4. Stem-and-leaf plot.
Worked example

Example 2: Choose a scale

A histogram of 40 students' heights will have bars with frequencies 3, 8, 14, 11 and 4. Choose a scale for the vertical axis.

  1. The tallest bar is 14, so the scale must go to at least 14.
  2. Counting by 1s would need 14 or more steps: crowded.
  3. Counting by 5s gives 0, 5, 10, 15. Only 3 steps, so values like 8 and 11 are hard to read.
  4. Counting by 2s gives 0, 2, 4, ..., 14 or 16. That's 7 or 8 steps: just right.

0 to 16 by 2s (0 to 14 by 2s also works). Start at 0.

Give and use helpful feedback

When you look at someone's graph, start with something that works ("Your title tells me exactly what it's about"). Then ask a question or make a suggestion ("Could you add a source?" "Why did you choose a broken-line graph?"). When you get feedback, listen, think about it, and decide what to change. Good graph makers revise!

Just for fun

Using a broken-line graph for favourite ice cream flavours is like using a fork to eat soup. It's a real tool... just not the right one for the job!

Hands-on activity

Graph makeover

You need: a flyer, newspaper, magazine or website with a graph (ask a grown-up to help you find one online), or a graph from one of your earlier lessons; grid paper.

  1. Look at the graph. What type is it? What job is it doing?
  2. Check it with the list: title? labels and units? a sensible scale starting at 0? legend? source?
  3. Was it the best type of graph for the data? Could another type do the job better?
  4. Redraw it, fixing anything that's missing. Write one sentence justifying your choice: "I chose a ______ because ______."
  5. Show a family member and ask for one piece of feedback.

Your turn

1

Which graph would you choose for the number of hours of daylight each week from January to June? Why?

2

Which graph would you choose for the favourite pizza topping of 30 students? Why?

3

Which graph would you choose for the arm spans of 80 students? Why?

4

Which graph would you choose to show how many students in each grade walk, bus or are driven to school, and the total for each grade?

5

A graph shows students' favourite fruit. It has a title and a scale, but no axis labels or source. What should be added?

6

Finish this justification: "I chose a histogram for the times to run 1 km because..."

More practice: warm-up

1

Which graph shows how continuous data changes over time?

2

Which graph has bars that touch?

3

Bar graph above: how many students chose sledding?

4

Why does a graph need a source?

5

Should the scale on a bar graph usually start at 0?

More practice: on your own

1

Choose a graph for the number of goals a hockey team scored in each of its 12 games, where you want to see every game's value and find the mode.

2

A bar graph's tallest bar is 38. Suggest a scale.

3

Mila made a broken-line graph of students' favourite sports. Give her helpful feedback.

4

Why is a histogram better than a bar graph for 60 students' heights?

5

Bar graph above: how many more students chose skating or sledding than chose skiing or snowshoeing?

Challenge

1

Natalie recorded the outside temperature at noon every day in January. She wants to show how the temperature changed during the month and how many days were in each temperature range. Which two graphs should she make? Justify.

2

The same data can sometimes be shown in more than one good way. Give a reason someone might choose a stem-and-leaf plot instead of a histogram for 20 quiz scores.

3

A histogram's frequencies are 2, 6, 25, 9 and 3. Explain why a scale counting by 2s would be a poor choice, and choose a better one.

Check your understanding

Quiz

1.

Which graph is best for showing the temperature every hour during a day?

2.

Which graph is best for comparing the favourite sports of Grade 5 and Grade 6 students?

3.

Which graph is best for the masses of 100 apples?

4.

A graph's tallest bar is 27. Which scale is best?

5.

Which is not needed on a single-colour bar graph?

6.

Which is a good justification?

For parents and teachers

What this lesson teaches: choosing the best type of graph for a data set, including histograms and broken-line graphs, giving every graph a proper title, labels, scale and source, and justifying the choice (D1.3). Giving and using feedback practises Strand A skills (A1).

How to help at home:

  • When you see a graph in the news or online, ask: "What job is this graph doing? Is it the right type?"
  • Ask your child to finish the sentence "I chose a ___ because ___" whenever they make a graph.
  • Model kind, specific feedback: one thing that works, one question or suggestion.

Common difficulties:

  • Choosing a graph because it looks nice rather than because it suits the data.
  • Choosing a scale from the smallest value, or one that makes bars tiny.
  • Forgetting the source and units.