Teach Me Maths

Pictograms, Bar Charts and Vertical Line Charts

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How to read and draw pictograms, bar charts, dual and composite bar charts and vertical line charts, using the key and the scale, finding a missing value from a total and using the numbers in a further calculation.

What the exam asks

Pictograms, bar charts and vertical line charts all show how many there are of each thing. A category is a group, such as a day or a type of drink. The frequency is how many there are in that group.

In the exam you are usually asked to read a value from a chart, find a total or work out how many more, for 1 or 2 marks. Harder parts give you a total and ask you to complete the chart, or to use the numbers to work out an amount of money or a fraction, for about 3 marks.

Before you work anything out, read the title, the labels on the axes, the key and the scale.

Pictograms and their key

A pictogram uses symbols to show frequencies. The key tells you how many one whole symbol represents.

Part of a symbol shows part of the key. With a key of 12, half a symbol represents 12\div2=6 and a quarter of a symbol represents 12\div4=3

If the key is missing, use a row whose total you know. If 3 whole symbols show 15, one symbol represents 15\div3=5

Worked example 1: Reading a pictogram

The pictogram shows the number of plants sold at a garden centre. How many plants were sold on Saturday?

  1. One whole square represents 4 plants. Saturday has 4 whole squares and a quarter of a square.
  2. The 4 whole squares represent 4\times4=16 plants
  3. A quarter of a square represents 4\div4=1 plant

  4. Your turn. How many plants were sold on Saturday?

    16+1=17

  5. Answer: 17 plants

Worked example 2: Showing a number on a pictogram

In a pictogram, one square represents 8 sandwiches. A café sold 26 sandwiches on Monday. Show this on the pictogram.

  1. Count in 8s: 3 whole squares represent 3\times8=24 sandwiches

  2. Your turn. How many sandwiches are still to show? Work out 26-24

    26-24=2

  3. 2 is a quarter of 8, because 8\div4=2. So the last symbol is a quarter of a square.
  4. Answer: 3 whole squares and a quarter of a square

Reading a bar chart

In a bar chart the height of each bar shows the frequency. The bars are all the same width, with gaps between them.

Work out what each grid line is worth before you read a bar. If the labels go 0, 10, 20, 30 and there is one grid line between each pair of labels, each line is worth 5

A bar can stop halfway between two grid lines. Its value is then halfway between the two numbers.

For a total, add the frequencies. For “how many more”, subtract the smaller frequency from the larger one.

Worked example 3: Reading between the grid lines

The bar chart shows the number of cars in a car park at 9 am on four days. How many more cars were there on Wednesday than on Tuesday?

  1. The scale goes up in 2s, so each grid line is worth 2
  2. Wednesday’s bar reaches the line for 12

  3. Your turn. Tuesday’s bar stops halfway between 8 and 10. What number does it show?

    Tuesday’s bar shows 9

  4. 12-9=3
  5. Answer: 3 more cars

Vertical line charts

A vertical line chart is used for data that are whole numbers, such as the number of pets each pupil owns. The numbers along the bottom are the values. The height of each line is the frequency: how many times that value happened.

Keep the values and the frequencies apart. The value with the tallest line is the mode. The heights of the lines added together give the total number of people.

Worked example 4: Using a vertical line chart

The vertical line chart shows the number of pets owned by each pupil in a class. How many pupils own 2 or more pets?

  1. 2 or more pets means 2, 3 or 4 pets.
  2. Read the heights of those three lines: 5, 3 and 1
  3. Add the frequencies, not the numbers of pets along the bottom.

  4. Your turn. Work out 5+3+1

    5+3+1=9

  5. Answer: 9 pupils

Dual and composite bar charts

A dual bar chart has two bars side by side for each category. The key tells you which bar is which.

Compare the two bars for one category. Pens went up from 6 in week A to 8 in week B, an increase of 2. Pads went down from 10 to 7, a decrease of 3

A composite bar chart stacks the parts of each category on top of each other in one bar. The top of each part is a running total, so find a part by subtracting the bottom of that part from its top.

Worked example 5: Reading a composite bar chart

The composite bar chart shows the fruit sold at a market stall on three days. How many pears were sold on Saturday?

  1. On Saturday, the pears section starts at 14 and ends at 22
  2. The top of the section, 22, is apples and pears together, not pears on their own. So subtract the bottom of the section from its top.

  3. Your turn. Work out 22-14

    22-14=8

  4. Answer: 8 pears

Drawing a bar chart

Label both axes. Give the frequency axis a scale that goes up in equal steps from 0, and label the grid lines, not the spaces between them.

Draw the bars with a ruler, all the same width and with equal gaps. For a dual or composite bar chart, add a key. Tell the bars apart with shading, not colours, because exam papers are marked in shades of grey, not in colour.

Be careful with a chart whose frequency scale does not start at 0. It makes a small difference look large, so read the actual numbers before you compare two bars.

Worked example 6: Finding a missing bar from a total

The bar chart shows some of the hot drinks sold at a stall on one day. 50 hot drinks were sold altogether. Each hot chocolate costs £2.50. Work out how much money was taken for hot chocolate.

  1. The labels go up in 4s, with a grid line halfway between each pair, so each grid line is worth 2. Tea shows 16 and coffee shows 22
  2. Tea and coffee together: 16+22=38

  3. Your turn. How many hot chocolates were sold?

    Hot chocolate: 50-38=12

  4. To complete the chart, draw the hot chocolate bar up to 12, the same width as the others.

  5. Your turn. Work out 12\times\pounds 2.50

    12\times\pounds 2.50=\pounds 30

  6. Answer: \pounds 30

Common mistakes

  • Counting a part symbol as 1. A part symbol is a fraction of the key: with a key of 8, a quarter of a symbol is 2
  • Taking each grid line to be worth 1. Work out what one grid line is worth from the labels before you read or draw a bar.
  • Reading the top of a composite section as its value. Subtract the bottom of the section from its top.
  • Mixing up the rows or the bars. Check that each row, bar and key matches the day or group in the question.
  • Drawing a scale with unequal steps or no labels. Go up in equal steps from 0 and label both axes.
  • Using colours to tell bars apart. Use shading and a key, because exam papers are marked in shades of grey.

Practice questions

More on this topic: Pictograms, Bar Charts and Vertical Line Charts worksheet with full solutions