Chapter 2 of 8

All 8 chapters
  1. 1Collecting data, readunderstood
  2. 2Bar charts and pie charts, readunderstood
  3. 3Mean, median and mode, readunderstood
  4. 4Comparing two groups, readunderstood
  5. 5Line graphs and honest charts, readunderstood
  6. 6The language of chance, readunderstood
  7. 7Working out chances, readunderstood
  8. 8Experiments and fair games, readunderstood

M3.7.2 Chapter 2

Bar charts and pie charts

Twelve of 36 children walk to school. How big is the walk sector of a pie chart?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Draw a bar chart for grouped data
  • Draw a pie chart by working out the angles
  • Read a pie chart to find fractions of the whole

Last chapter you sorted answers into classes and counted them. Now we draw the counts. A bar chart shows how many are in each class. A pie chart shows how a whole is shared out.

Draw it first

Draw a bar chart for the classes

  1. Step 1: a chart with a scale from 0 to 10 in steps of 2 and the classes 0 to 9, 10 to 19 and 20 to 29 along the bottom. Step 2: a bar for each class. The bars are 9, 7 and 4 high. The axis labels are books read and children.02468100to 910to 1920to 29books readchildren

    1 Draw the axes. Put the scale on the side, going up in equal steps from 0. Write each class under its place.

  2. Step 1: a chart with a scale from 0 to 10 in steps of 2 and the classes 0 to 9, 10 to 19 and 20 to 29 along the bottom. Step 2: a bar for each class. The bars are 9, 7 and 4 high. The axis labels are books read and children.02468100to 910to 1920to 29books readchildren

    2 Draw a bar for each class, as high as its count. Leave a gap between the bars.

Why the gap? Counted data jumps from 9 to 10 with nothing between. The gap shows that. Bars for measured classes touch, because measured data has no jump. Always start the scale at 0, and make every step the same size.

A bar chart of measured data. The axis labels are height in cm and plants. The classes are 10 up to 20, 20 up to 30 and 30 up to 40, and the numbers 10, 20, 30 and 40 are written where the bars meet. The bars touch. They are 4, 9, 5 high.024681049510203040height in cmplants
Heights of 18 plants. A plant of 20 cm goes in the second bar. The bars touch, so no height falls in a gap.

Worked example

A frequency table shows 9, 7 and 4 children in three classes. The classes are 0 to 9, 10 to 19 and 20 to 29. Choose a scale for the bar chart. How high is each bar?

  1. The biggest count is 9, so a scale up to 10 is enough.
  2. Go up in steps of 2. From 0 to 10 that is 10 ÷ 2 = 5 steps, so the chart is not crowded.
  3. The bars reach 9, 7 and 4. The bar for 9 stops halfway between the lines for 8 and 10.

Answer: The bars are 9, 7 and 4 high.

A bar chart. The axis labels are books read and children. The scale goes from 0 to 10 in steps of 2. The classes are 0 to 9, 10 to 19 and 20 to 29. The bars are 9, 7, 4.024681090to 9710to 19420to 29books readchildren
The same bar chart, with each count written on top of its bar.

A bar chart is good for comparing classes. A pie chart is good when the parts make one whole, such as how 36 children travel. A whole turn is 360°. Each child gets the same share of that turn.

Draw it first

Draw a pie chart for 36 children

  1. Step 1: a table of how children travel. Way and Children. walk 12, bus 6, bicycle 9, car 9. Step 2: the table gets a third column, Angle: walk 120°, bus 60°, bicycle 90°, car 90°. Step 3: a pie chart with four sectors: walk 120°, bus 60°, bicycle 90°, car 90°.WayChildrenwalk12bus6bicycle9car9

    1 Count each group and add them: 12 + 6 + 9 + 9 = 36 children.

  2. Step 1: a table of how children travel. Way and Children. walk 12, bus 6, bicycle 9, car 9. Step 2: the table gets a third column, Angle: walk 120°, bus 60°, bicycle 90°, car 90°. Step 3: a pie chart with four sectors: walk 120°, bus 60°, bicycle 90°, car 90°.WayChildrenAnglewalk12120°bus660°bicycle990°car990°

    2 One child is 360 ÷ 36 = 10°. Multiply each count by 10 to get its angle.

  3. Step 1: a table of how children travel. Way and Children. walk 12, bus 6, bicycle 9, car 9. Step 2: the table gets a third column, Angle: walk 120°, bus 60°, bicycle 90°, car 90°. Step 3: a pie chart with four sectors: walk 120°, bus 60°, bicycle 90°, car 90°.walk120°bus60°bicycle90°car90°

    3 Draw a circle. Draw each sector with its angle. Name every sector.

The rule is: angle = count ÷ total × 360°. A sector is one slice of the circle. Each sector has its own pattern and its own name. So the chart works on a black and white copy.

Worked example

Kofi asked 20 children for their favourite sport. 8 chose cricket, 6 running, 4 swim and 2 other. Work out the angle of each sector.

  1. There are 8 + 6 + 4 + 2 = 20 children in all.
  2. One child is 360 ÷ 20 = 18°.
  3. Cricket is 8 × 18 = 144°. Running is 6 × 18 = 108°.
  4. Swim is 4 × 18 = 72°. Other is 2 × 18 = 36°.
  5. Check: 144 + 108 + 72 + 36 = 360.

Answer: 144°, 108°, 72° and 36°

A pie chart of favourite sports. cricket 144°, running 108°, swim 72°, other 36°.cricket144°running108°swim72°other36°
Kofi's pie chart. The four angles add up to 360°, one whole turn.

You can also read a pie chart. A sector's angle out of 360° is its fraction of the whole. A right angle of 90° is 1/4 of the circle. A straight angle of 180° is 1/2.

Worked example

The pie chart shows the favourite fruit of 24 children. The mango sector is 90°. What fraction of the children chose mango, and how many children is that?

  1. One child is 360 ÷ 24 = 15°.
  2. The mango sector is 90°, so 90 ÷ 15 = 6 children.
  3. As a fraction: 90 out of 360 is 1/4.
  4. Check: 1/4 of 24 children is 24 ÷ 4 = 6.

Answer: 1/4, which is 6 children

A pie chart of favourite fruit. mango 90°, banana 120°, orange 60°, apple 90°.mango90°banana120°orange60°apple90°
Favourite fruit of 24 children. The mango sector is a quarter of the circle.

See it three ways

With things

Ana shares a round bread. Kofi gets half. Mei and Leila get a quarter each. The pieces meet at the middle.

As a picture

A pie chart of a shared bread. Kofi 180°, Mei 90°, Leila 90°.Kofi180°Mei90°Leila90°

In symbols

Half of 360° is 180°. A quarter of 360° is 90°. 180° + 90° + 90° = 360°.

Try it

Fold a pie chart

You need: a round piece of paper, a pencil.

  1. Fold the paper circle in half. Fold it in half again. Fold it once more.
  2. Open it. The folds make 8 equal sectors.
  3. Each sector is 360 ÷ 8 = 45°. Write red in 4 sectors, blue in 2 and white in 2.
  4. Check that the angles add up to 360°.

What you will see: Red takes half the circle, 180°. Blue and white take 90° each. Each fold made a sector the same size.

If you cannot try it, this is what happens.
A pie chart made from the folded circle. red 180°, blue 90°, white 90°.red180°blue90°white90°

A wrong idea many people have

The angle of a sector is the same as its count. 12 children make a sector of 12°.

Why it feels right: The count is the number you can see, so it feels natural to use it.

The test that breaks it: Add up the angles that way: 12 + 6 + 9 + 9 = 36. A pie chart must add up to 360°, so something is wrong.

What is true: The angle is count ÷ total × 360. Here that is 12 ÷ 36 × 360 = 120°.

Key words

bar chart
a chart with one bar for each class, as high as its count.
pie chart
a circle cut into sectors, one for each part of a whole.
sector
one slice of a circle, drawn with an angle.

Back to your guess

The answer is B: 120°

The whole circle is 360° and there are 36 children in all. One child is 360 ÷ 36 = 10°. So 12 children is 12 × 10 = 120°.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Mei asked 24 children for their favourite food. 6 chose rice. What is the angle of the rice sector?

    Tap your answer.

    1. Yes, that is right. One child is 360 ÷ 24 = 15°. Six children is 6 × 15 = 90°.

    2. Not this one. 15° is the angle for one child. The rice sector holds 6 children, so multiply by 6. Go to M3.7.2. Try another.

    3. Not this one. That is the count, not the angle. Work out one child first: 360 ÷ 24 = 15°. Go to M3.7.2. Try another.

    See the answer

    90°

    One child is 360 ÷ 24 = 15°. Six children is 6 × 15 = 90°.

    • If you chose B: 15° is the angle for one child. The rice sector holds 6 children, so multiply by 6. Go to M3.7.2.
    • If you chose C: That is the count, not the angle. Work out one child first: 360 ÷ 24 = 15°. Go to M3.7.2.

  2. Which class has the most children in this bar chart?

    A bar chart. The axis labels are books read and children. The classes are 0 to 9, 10 to 19 and 20 to 29. The bars are 9, 7, 4.02468100to 910to 1920to 29books readchildren
    Tap your answer.

    1. Not this one. The class 20 to 29 has the biggest numbers of books, but the fewest children. The class with the most children has the tallest bar. Go to M3.7.2. Try another.

    2. Not this one. 9 is the height of the tallest bar. The question asks for the name of the class under it. Go to M3.7.2. Try another.

    3. Yes, that is right. The tallest bar is the first one, and it stands over the class 0 to 9.

    See the answer

    0 to 9

    The tallest bar is the first one, and it stands over the class 0 to 9.

    • If you chose A: The class 20 to 29 has the biggest numbers of books, but the fewest children. The class with the most children has the tallest bar. Go to M3.7.2.
    • If you chose B: 9 is the height of the tallest bar. The question asks for the name of the class under it. Go to M3.7.2.

  3. Which bar chart should have a gap between its bars?

    Tap your answer.

    1. Not this one. Heights are measured, so they run on with no jump from one class to the next. The bars touch. Go to M3.7.2. Try another.

    2. Yes, that is right. Counted data jumps from one whole number to the next, so its bars have a gap. Measured data has no jump, so its bars touch.

    3. Not this one. Books read is counted data. It jumps from 9 to 10 with nothing between, so its bars stand apart. Go to M3.7.1. Try another.

    See the answer

    A chart of the number of books each child read, grouped into classes

    Counted data jumps from one whole number to the next, so its bars have a gap. Measured data has no jump, so its bars touch.

    • If you chose A: Heights are measured, so they run on with no jump from one class to the next. The bars touch. Go to M3.7.2.
    • If you chose C: Books read is counted data. It jumps from 9 to 10 with nothing between, so its bars stand apart. Go to M3.7.1.

  4. In the travel pie chart the walk sector is 120°. What fraction of the children walk?

    A pie chart of how 36 children travel. walk 120°, bus 60°, bicycle 90°, car 90°.walk120°bus60°bicycle90°car90°
    Tap your answer.

    1. Yes, that is right. 120 out of 360 is 1/3, because 360 ÷ 120 = 3.

    2. Not this one. Half of the circle is 180°. The walk sector is smaller than that. Go to M3.7.2. Try another.

    3. Not this one. 12 is the number of children who walk. The fraction uses the angle: 120 out of 360. Go to M3.7.2. Try another.

    See the answer

    1/3

    120 out of 360 is 1/3, because 360 ÷ 120 = 3.

    • If you chose B: Half of the circle is 180°. The walk sector is smaller than that. Go to M3.7.2.
    • If you chose C: 12 is the number of children who walk. The fraction uses the angle: 120 out of 360. Go to M3.7.2.

  5. Why must the angles of a pie chart always add up to 360°?

    Tap your answer.

    1. Not this one. Sectors can be any size. Only the total is fixed. It is one whole turn. Go to M3.7.2. Try another.

    2. Not this one. The number of children changes from survey to survey. The angles are scaled so they always fill the circle. Go to M3.7.2. Try another.

    3. Yes, that is right. A pie chart shows one whole shared out. A whole is one full turn, which is 360°.

    See the answer

    Together the sectors make one whole turn of the circle.

    A pie chart shows one whole shared out. A whole is one full turn, which is 360°.

    • If you chose A: Sectors can be any size. Only the total is fixed. It is one whole turn. Go to M3.7.2.
    • If you chose B: The number of children changes from survey to survey. The angles are scaled so they always fill the circle. Go to M3.7.2.

  6. In the travel pie chart, the bus sector is 60°. How many of the 36 children take the bus?

    Tap your answer.

    1. Not this one. That is the angle, and it is more than the 36 children in all. Divide the angle by 10, the angle of one child. Go to M3.7.2. Try another.

    2. Yes, that is right. One child is 360 ÷ 36 = 10°. The bus sector is 60°, and 60 ÷ 10 = 6 children.

    3. Not this one. 10° is the angle of one child. Divide 60° by it to count the children. Go to M3.7.2. Try another.

    See the answer

    6 children

    One child is 360 ÷ 36 = 10°. The bus sector is 60°, and 60 ÷ 10 = 6 children.

    • If you chose A: That is the angle, and it is more than the 36 children in all. Divide the angle by 10, the angle of one child. Go to M3.7.2.
    • If you chose C: 10° is the angle of one child. Divide 60° by it to count the children. Go to M3.7.2.

  7. Priya asked 30 children which game they like best. 5 chose football. What is the angle of the football sector?

    See the answer

    60°

    One child is 360 ÷ 30 = 12°. Five children is 5 × 12 = 60°.

  8. A pie chart has a sector of 45°. What fraction of the circle is it?

    See the answer

    1/8

    45 out of 360 is 1/8, because 360 ÷ 45 = 8.

  9. From an earlier chapter

    Review: classes are 0 to 9, 10 to 19 and 20 to 29. In which class does the answer 14 go?

    See the answer

    10 to 19

    14 is at least 10 and at most 19, so it fits the class 10 to 19. Classes have no gap and no overlap.

Keep it

Copy this into your exercise book.

A bar chart starts at 0, has equal steps and a gap between bars. A pie chart sector is count ÷ total × 360°. Sector angles add up to 360°. A sector of 90° is a quarter.

Draw: Draw a circle cut into sectors of 180°, 90° and 90°. Name each sector and write its angle.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (968 KB). It opens on any phone.