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Picture graphs

Statistics and data · level 1, lesson 3 of 5

A question to start

Some children each put a sticker on a big sheet of paper to show their favourite fruit. Apples got the big orange stickers. Grapes got the little green stickers. Here is the sheet.

apple grapes

Which fruit won? The apple row looks much longer. But count: apples have 4 stickers, grapes have 5. Grapes won!

The sheet tricked us, because the apple stickers were bigger and stuck far apart, and the grape stickers were small and squashed together. In this lesson you learn how to make a picture graph that can never trick anyone like that.

The idea

What a picture graph is

A graph is a picture that shows numbers, so you can see them quickly without reading a list. A picture graph uses one small picture, or one sticker, for each thing you counted.

For a picture graph about favourite fruit, each child gets one sticker. They put it in the row for the fruit they like best. So each sticker stands for one child.

The rules that make it fair

A picture graph is fair when you can compare the rows just by looking at how long they are. For that, it needs four things.

  1. Every sticker the same size. A big sticker must not look like more than a small one.
  2. Every row starts at the same line. Like runners in a race, everyone starts at the starting line.
  3. The stickers are spaced the same. No squashing, no stretching. A grid of boxes, one sticker in each box, makes this easy.
  4. Every row has a name (a label), so you know what it stands for. The whole graph also gets a name at the top, called the title, so you know what question it answers.

Here is the fruit sheet again, done the fair way, with every choice on it. Fourteen children each put one sticker in one box.

Our favourite fruit apple banana pear grapes

Now the rows tell the truth at a glance. The grapes row is longest, so grapes are the favourite. The banana row is shortest. You can still count to be sure: apple 4, banana 2, pear 3, grapes 5.

Why lining up works

Look at the apple row and the grapes row. They start at the same line, and every sticker sits in a box the same size. So the first apple sticker is right above the first grapes sticker, the second above the second, and so on. Each apple sticker has a grapes partner. But the grapes row has one sticker left over at the end. That is why the grapes row is longer: it has one more.

This is the "lining up" idea from the last lesson, built into a picture. The boxes do the lining up for you. A longer row always means more, and a shorter row always means fewer. That is the whole reason picture graphs are drawn this way.

Rows or columns

You can draw the rows going across, as above, or you can stand them up, like towers. Rows standing up are called columns.

Our favourite fruit apple banana pear grapes

This is the same data, turned. Now the starting line is at the bottom, like the ground. The tallest tower is the favourite. The rules are the same: same size stickers, same spacing, every column starts at the bottom line, every column has a label.

Both ways are correct. Choose whichever fits on your paper.

Making a picture graph, step by step

  1. Write the title. What question does the graph answer? ("Our favourite fruit")
  2. Draw the starting line and a row of boxes for each choice.
  3. Label each row with its choice.
  4. One sticker per child, one sticker per box, starting next to the line, no gaps.
  5. Check the total. Count all the stickers. It should equal the number of children who answered.

For the fruit graph: 4 and 2 make 6, and 3 more make 9, and 5 more make 14. Fourteen children answered, so the graph is complete.

A picture graph keeps every answer

Here is something nice about picture graphs. Each sticker is one real child. If you wrote each child's name on their sticker, you could even find out who chose what. Nothing is lost. The graph is just the children's answers, sorted into rows and lined up.

Worked examples

Example 1. From a list to a graph. Ten children said their favourite colour: red, blue, blue, green, red, blue, yellow, blue, red, green. Make a picture graph.

  1. Sort and count: red 3, blue 4, green 2, yellow 1.
  2. Total check: 3 and 4 make 7, and 2 more make 9, and 1 more makes 10. Ten children. Good.
  3. Draw a starting line and four rows of boxes, labelled red, blue, green, yellow.
  4. Put one sticker in a box for each child: 3 in the red row, 4 in blue, 2 in green, 1 in yellow.
Our favourite colour red blue green yellow

Read it: blue has the longest row, so blue is the favourite colour. Yellow has the shortest row.

Example 2. Fixing an unfair graph. Look again at the messy fruit sheet at the top of this page. What was wrong, and how do you fix it?

  1. The apple stickers were bigger than the grape stickers. Fix: use the same size sticker for every child.
  2. The apple stickers were far apart and the grape stickers were squashed together. Fix: draw boxes, one sticker in each box, all boxes the same size.
  3. Did the rows start at the same line? Yes, so that part was fine.
  4. Redrawn fairly, the grape row (5 stickers) is longer than the apple row (4 stickers), as it should be.

Example 3. Rows into columns. Turn the colour graph from example 1 into a column graph.

  1. Draw a line along the bottom. That is the starting line now.
  2. Write red, blue, green, yellow under the line, spaced out.
  3. Above red, stack 3 stickers. Above blue, stack 4. Above green, 2. Above yellow, 1.
  4. The tallest column is blue, the shortest is yellow. Turning the graph did not change any count. It only changed which way the rows point.

Try it

  1. Look at the fruit picture graph. How many children chose banana?
  2. In the fruit picture graph, which fruit was chosen by the fewest children?
  3. A picture graph about pets has a dog row with 6 stickers and a cat row with 6 stickers. What can you say?
  4. Jay drew a picture graph, but his cat row starts further to the right than his dog row. Why is that a problem?
  5. Eight children voted for a game: tag, tag, hide-and-seek, tag, ball, hide-and-seek, tag, ball. Sort and count the votes. Which game would have the longest row in a picture graph?
  6. A column graph about weather shows the sunny column is 5 stickers tall, the rainy column is 2 stickers tall and the snowy column is 0 stickers tall. What does the snowy column look like? How many days were counted in all?
  7. Why should every sticker in a picture graph be the same size?
Answers
  1. 2 children.
  2. Banana, with only 2 stickers.
  3. The two rows are the same length. The same number of children chose dog and cat: 6 each.
  4. If the cat row starts further along, it will look longer than it really is. Every row must start at the same line, so that a longer row really means more.
  5. Tag 4, hide-and-seek 2, ball 2. Check: 4 and 2 and 2 make 8. Tag would have the longest row.
  6. The snowy column has no stickers at all: just its label under the line. There were 0 snowy days. Days counted: 5 and 2 make 7, and 0 more is still 7 days.
  7. So that each sticker looks like the same amount. Each sticker stands for one child. If some stickers were bigger, those rows would look like more children than they really are.

Common mistake

Making the stickers different sizes or spacing them unevenly. Then the longest row might not be the biggest number. Use one size of sticker and a grid of equal boxes.

Starting the rows in different places. A row that starts late, or starts early, will look shorter or longer than it should. Every row begins at the same starting line.

Where it leads