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Reading a picture graph

Statistics and data · level 1, lesson 5 of 5

A question to start

Here is a class's picture graph. Each sticker is one child.

Our favourite pets dog cat fish hamster

"How many more children chose dogs than cats?"

Lots of people answer 7, because the dog row has 7 stickers. Some people answer 11, because 7 and 4 make 11. But the question was "how many more". The answer is 3. In this lesson you find out why, and you learn to read everything a picture graph can tell you, and to notice what it cannot tell you.

The idea

Reading one row

Each row has a label and some stickers. Count the stickers in a row and you know how many children chose that answer.

  • Dog: 7 children.
  • Cat: 4 children.
  • Fish: 2 children.
  • Hamster: 3 children.

Always check the title first. It tells you what the graph is about. This one is "Our favourite pets", so each sticker is a child who chose that pet as their favourite.

Most and fewest

The longest row is the answer chosen most often. The shortest row is the answer chosen fewest times.

  • Most: dog, with 7.
  • Fewest: fish, with 2.

You can see this without counting, because the rows start at the same line and the stickers are lined up. That is the whole point of drawing a picture graph carefully.

How many more?

"How many more chose dogs than cats?" means: how many extra dog stickers are there, after every cat sticker has a dog partner?

cat dog 3 extra

Look down from each cat sticker to the dog sticker below it. The first 4 dog stickers each have a cat partner. The dog stickers with no partner are the extra ones, inside the dashed box. There are 3 of them.

So 3 more children chose dogs than cats.

You can also find it with numbers. Start at the smaller count and count up to the bigger one. From 4, count up to 7: 5, 6, 7. That is 3 steps. The same answer.

How many fewer?

"How many fewer chose cats than dogs?" is the same question turned around. The cat row is 3 stickers short of the dog row. So 3 fewer children chose cats. "3 more dogs than cats" and "3 fewer cats than dogs" say the same thing.

How many altogether?

To find how many children answered, count all the stickers, or add up the rows.

  • 7 and 4 make 11.
  • 11 and 2 make 13.
  • 13 and 3 make 16.

16 children answered. If there are 16 children in the class, everybody answered once.

You can also ask "how many chose dog or cat?" That means: add those two rows. 7 and 4 make 11.

What the graph does NOT tell us

A picture graph tells us a lot, but not everything. Good data readers always ask: what can't this graph tell me?

This pet graph does not tell us:

  • Why each child chose their pet. Maybe some love dogs because they have one. We were never told.
  • Who chose what. The stickers have no names.
  • Whether the children have that pet at home. The question was about a favourite pet, not about the pets they own.
  • What other classes think. This is only one class. Another class might love cats.
  • What children who were away that day would choose.
  • That nobody likes rabbits. Rabbit was not one of the rows. Maybe rabbit was not a choice, so nobody could pick it.

It is very tempting to read more into a graph than it says. "Dogs are the best pets" is not what this graph shows. What it shows is: "In this class, on that day, more children chose dog than any other pet on the list." Saying exactly what the data shows, and no more, is the most important habit in statistics.

Careful with "most"

Dog is the most popular pet. But did most of the children choose dog? Most of the children would mean more than half. 7 children chose dog, and 9 did not (4 and 2 and 3 make 9). So more children did not choose dog than did! The honest sentence is "dog was chosen more than any other pet", not "most children like dogs best".

Worked examples

Example 1. Reading a weather graph. A class put one sticker on a graph each day for 15 school days.

Weather for 15 days sunny cloudy rainy snowy
  1. Sunny: 6 days. Cloudy: 5 days. Rainy: 3 days. Snowy: 1 day.
  2. Most: sunny. Fewest: snowy.
  3. How many more sunny days than rainy days? From 3, count up to 6: 4, 5, 6. 3 more.
  4. Altogether: 6 and 5 make 11, and 3 more make 14, and 1 more makes 15 days. That matches the 15 days.

Example 2. Two questions, two answers. Use the weather graph. "How many days were rainy or snowy?" and "How many more cloudy days than snowy days?"

  1. Rainy or snowy: add the two rows. 3 and 1 make 4 days.
  2. Cloudy compared with snowy: from 1, count up to 5: 2, 3, 4, 5. That is 4 more.

Notice that both answers are 4, but they answer different questions. "Or" means put together. "How many more" means find the difference.

Example 3. What can we say? Here are some sentences about the pet graph. Which ones does the graph really show?

  1. "Dog was chosen by 7 children." Yes: count the dog row.
  2. "Fish was the least popular choice in this class." Yes: the fish row is shortest.
  3. "Children everywhere like dogs best." No: the graph is only about this one class.
  4. "Ava chose a hamster." No: the stickers have no names, so we cannot tell who chose what.
  5. "The children chose dogs because dogs are friendly." No: the graph does not say why anyone chose anything.

Try it

Use the pet graph at the top of this page for questions 1 to 5.

  1. How many children chose hamster?
  2. How many more children chose hamster than fish?
  3. How many children chose cat or fish?
  4. Two more children arrive late and both choose fish. Now which pet is the fewest?
  5. Is this true: "The graph shows that nobody in the class likes rabbits"? Explain.

Use the weather graph for questions 6 and 7.

  1. How many fewer snowy days than cloudy days were there?
  2. Liam says, "It was sunny on most days." Is he right? (Hint: how many days were not sunny?)
  3. A picture graph about favourite colours has a red row of 5 and a blue row of 8. Without drawing, how many more chose blue than red? How many chose red or blue?
Answers
  1. 3 children.
  2. From 2, count up to 3: just 1 step. 1 more.
  3. 4 and 2 make 6 children.
  4. The fish row grows from 2 to 4. Now cat has 4 and fish has 4: they are tied. Hamster, with 3, is now the fewest.
  5. Not true. Rabbit was not a row on the graph, so maybe it was not one of the choices. Also, a child can like rabbits but like another pet even more. The graph only shows each child's favourite from the list.
  6. Cloudy 5, snowy 1. From 1 count up to 5: 2, 3, 4, 5. 4 fewer snowy days.
  7. No. 6 days were sunny, but 5 and 3 and 1 make 9 days were not sunny. More days were not sunny than sunny. He can say "sunny was the most common weather", but not "it was sunny on most days".
  8. From 5 count up to 8: 6, 7, 8. 3 more chose blue. Red or blue: 5 and 8 make 13.

Common mistake

Answering "how many more" with the bigger number, or with the two numbers added. "How many more dogs than cats" is the number of extra dogs: the stickers with no partner. Count up from the smaller number to the bigger one.

Saying more than the graph shows. A graph about one class on one day does not tell you about everyone, about why people chose, or about choices that were not on the list. Say exactly what the data shows.

Where it leads