Skip to content
Cambridge IGCSE0580

Statistical charts and diagrams

Mathematics 0580 Chapter Notes

What this chapter covers

Statistical charts and diagrams
ShareWhatsAppPost
Statistical charts and diagrams notes

Read online free. Download a watermarked copy with a free account.

Read the notes

The full Statistical charts and diagrams notes as text: skim, search, and jump between subtopics.

~10 min read

In this chapter

  1. 1Bar charts
  2. 2Pictograms
  3. 3Frequency tables
  4. 4Drawing a pie chart
  5. 5Reading a pie chart
  6. 6Drawing a stem-and-leaf diagram
  7. 7Reading a stem-and-leaf diagram

1. Bar charts

In a bar chart every bar has the same width, with equal gaps between them. The height of a bar is the frequency, read from the scale on the vertical axis.

In a composite (stacked) bar chart each bar is split into parts. The size of one part is the difference between its top and its bottom. In a dual (side-by-side) bar chart each category has two bars next to each other.

When a bar is missing, find its height from the total: total frequency minus the bars already drawn.

Examiner insight

“Candidates had to correctly identify the heights of the 3 given bars and then subtract this total from 40 to find the height of the bar for senior tickets.” “Occasionally the final bar was the wrong height or the gaps between the bars were not consistent.”

Worked example 13 marks

30 people choose their favourite pet. 11 choose dogs, 9 choose cats and 4 choose fish. The rest choose rabbits. A bar chart has bars for dogs, cats and fish. Complete the bar chart for rabbits.

  1. 1

    people already shown: 11 + 9 + 4 = 24 [1]

  2. 2

    rabbits: 30 - 24 = 6, so the bar height is 6 [1]

  3. 3

    draw the bar for rabbits to height 6, with the same width as the other bars [1]

2. Pictograms

A pictogram uses a symbol to stand for a number of items. The key says how many items one whole symbol stands for.

To find a frequency, count the symbols and multiply by the key. A part symbol stands for the same fraction of the key: half a symbol is half of the key value.

To draw a row from a frequency, divide by the key to find how many symbols to draw.

Examiner insight

“However a large proportion of candidates left the space blank, maybe not sure where the key was on a pictogram.” “Common errors included answers from 40 + 25 or 1.5 from not using the key.”

Worked example 12 marks

In a pictogram, the key says that one whole symbol represents 4 books. On Monday there are 3 whole symbols and 1 half symbol. How many books does this represent?

  1. 1

    half a symbol represents 4 ÷ 2 = 2 books [1]

  2. 2

    3 × 4 + 2 = 14 books [1]

3. Frequency tables

A simple frequency distribution lists each value with its frequency: how many times it occurs. A tally records the count as marks, and the frequency is the total of the tally.

The frequencies add up to the number of items. Use this to check the table.

A frequency is a count, so it is a whole number.

Examiner insight

“Many did not use the words given in the question to complete the table and just completed the frequency column for the tally marks already given.” “Candidates must remember the context of a question; all the heights of the bars had to be whole numbers as this was the number of people who gave each score.”

Worked example 12 marks

The scores of 10 students in a quiz are 3, 4, 3, 5, 4, 3, 2, 4, 3, 5. Complete the frequency table.

scorefrequency
2
3
4
5
  1. 1

    count each score: 2 occurs once, 3 occurs four times, 4 occurs three times, 5 occurs twice

  2. 2

    frequencies 1, 4, 3, 2 [1]

  3. 3

    check: 1 + 4 + 3 + 2 = 10, the number of students [1]

4. Drawing a pie chart

In a pie chart the whole circle, 360^(°), stands for the total frequency. Each sector angle is in proportion to its frequency.

Find the angle for one item first: 360^(°) divided by the total. Then multiply by each frequency. The angles must add up to 360^(°).

Draw each sector with a protractor, and label each sector.

sector angle = frequency/(total frequency) × 360^(°)

Examiner insight

“Most found the total but some left this as their answer, while after the correct fraction written quite a few multiplied by 100 instead of 360°.” “With the pie chart, the most common errors were to not label sectors, or to misread protractor scales.”

Worked example 12 marks

The table shows information about the favourite drink of each of 60 students. Complete the table.

favourite drinknumber of studentspie chart angle
tea24144°
chocolate4
coffee32
  1. 1

    one student is 360 ÷ 60 = 6^(°)

  2. 2

    chocolate: 4 × 6 = 24^(°) [1]

  3. 3

    coffee: 32 × 6 = 192^(°) [1]

  4. 4

    check: 144 + 24 + 192 = 360

5. Reading a pie chart

A sector is the fraction angle ÷ 360 of the whole. Multiply that fraction by the total to find the number of items in the sector.

When a question asks for a fraction, give a fraction in its simplest form.

The angle is not the number of items. The angle only gives the share.

number in sector = (sector angle)/360 × total

Examiner insight

“However, some candidates equated the number of cars to the angle and gave the incorrect answer of 90.” “Many gave the fraction that spoke Portuguese, rather than the fraction that did not speak it.”

Worked example 12 marks

Ede asks 40 students if they prefer to drink water, juice or milk. She represents the results on a pie chart. The number of students who prefer milk is represented by a sector angle of 63°. Calculate the number of students who prefer milk.

  1. 1

    the sector is 63/360 of the 40 students

  2. 2

    63/360 × 40 [1]

  3. 3

    = 7 [1]

6. Drawing a stem-and-leaf diagram

In a stem-and-leaf diagram each number is split. For two-digit numbers the tens digit is the stem and the units digit is the leaf: 17 goes in the row for stem 1, with leaf 7.

Put the leaves in order, smallest first, in every row. Write a key that shows what one entry means, such as 1 | 7 represents 17.

Count the leaves at the end: there must be one for every value.

Examiner insight

“Some did not appear familiar with the topic as they entered the whole numbers in the leaf section of the diagram.” “Candidates should be encouraged to count to check that they have the correct number of data values in their diagram.”

Worked example 12 marks

A school records the number of students who are late on each of 12 days.

17 1 23 14 18 8 8 12 10 5 22 19

Complete the stem-and-leaf diagram. key: 1 | 7 represents 17 students

stemleaves
0
1
2
  1. 1

    tens digit is the stem, units digit is the leaf

  2. 2

    leaves in the order given: 0 | 1 8 8 5, 1 | 7 4 8 2 0 9, 2 | 3 2 [1]

  3. 3

    put each row in order: 0 | 1 5 8 8, 1 | 0 2 4 7 8 9, 2 | 2 3 [1]

  4. 4

    check: 4 + 6 + 2 = 12 days

7. Reading a stem-and-leaf diagram

Read an entry as stem and leaf together, using the key. In the row 24 with leaf 1, and key 23 | 3 represents 233 cm, the value is 241 cm.

The number of leaves is the number of values. To count values below a limit, read the rows in order and stop at the limit.

Give a fraction as a fraction of all the values, in its simplest form.

Examiner insight

“A very common answer was 2 either because candidates forgot they needed to include the 2 from the stem (making 22) or because 2 was the most common digit in the entire diagram.” “The most common error in part (b) was to give the number 4 from the table rather than the value of 24 which it represents.”

Worked example 12 marks

The lengths, in centimetres, of 32 wooden planks are given in the table as a stem-and-leaf diagram. key: 23 | 3 represents 233 cm. Find the fraction of all these planks which are less than 236 cm. Write your answer as a fraction in its simplest form.

stemleaves
233 4 4 5 6 6 8 9
240 0 1 1 1 1 3 6 8 8 9
252 3 5 6 7 9 9 9
260 0 1 2 4
  1. 1

    below 236 cm: 233, 234, 234, 235, so 4 planks [1]

  2. 2

    4/32 = 1/8 [1]

Recap

  • Bar chart: bars of equal width, height = frequency. A missing bar = total minus the other bars.
  • Composite bar chart: one bar split into parts. Dual bar chart: two bars side by side.
  • Pictogram: frequency = number of symbols × the value in the key.
  • Frequency table: the frequencies add up to the number of items.
  • Pie chart angle = frequency ÷ total × 360°. Angles add up to 360°. Label every sector.
  • Number in a sector = angle ÷ 360 × total.
  • Stem-and-leaf: leaves in order, a key, and read stem and leaf together.
  • Count the leaves to check that no value is missing.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. In a pictogram, one whole symbol represents 6 cars. Wednesday has 4 whole symbols and 1 half symbol. How many cars does Wednesday show?2 marks
  2. Do not use a calculator. A pie chart is drawn for 90 students. The sector for travelling by bus has an angle of 120°. How many students travel by bus?2 marks
  3. Do not use a calculator. 36 people choose a fruit: 12 choose apples, 18 choose bananas and 6 choose pears. Work out the sector angle for each fruit in a pie chart.3 marks
  4. Draw an ordered stem-and-leaf diagram for these 9 numbers, with a key. 34 41 38 45 31 38 52 40 473 marks
  5. The times, in minutes, that people wait are given in the table as a stem-and-leaf diagram. key: 1 | 2 represents 12 minutes. Write down (a) the shortest time, (b) the number of people who waited more than 25 minutes. | stem | leaves | | --- | --- | | 1 | 2 5 5 9 | | 2 | 0 3 3 6 8 | | 3 | 1 4 |2 marks
  6. In a composite bar chart, the bar for June has a swimming part from 0 to 7 hours and a running part from 7 to 18 hours. How many hours are spent running in June?2 marks
  7. 240 pupils choose a sport. A pie chart has a sector of 105° for football and 75° for rugby. All the rest choose tennis. How many pupils choose tennis?3 marks
  8. Do not use a calculator. 45 people choose a colour: 15 choose red, 10 choose blue and 20 choose green. (a) Work out the sector angle for each colour. (b) Write the fraction who chose blue in its simplest form.4 marks
  9. A pie chart of the favourite snacks of some children has sector angles of 96° for fruit, 36° for nuts and 78° for crisps. The rest is for chocolate. 10 more children chose fruit than chose nuts. Work out (a) the number of children, (b) the number who chose chocolate, (c) the fraction who chose chocolate, in its simplest form.6 marks
  10. Do not use a calculator. The masses, in kg, of 24 parcels are given in the table as a stem-and-leaf diagram. key: 2 | 4 represents 2.4 kg. (a) How many parcels have a mass of less than 3.3 kg? (b) A pie chart has one sector for each row. Work out the sector angle for the row with stem 3. (c) Six more parcels, each between 5.0 kg and 5.9 kg, are added and the pie chart is redrawn. Work out how many degrees bigger or smaller the sector angle for stem 3 becomes. | stem | leaves | | --- | --- | | 2 | 4 6 6 8 9 | | 3 | 0 1 3 3 5 7 7 8 9 | | 4 | 0 2 2 5 6 8 | | 5 | 1 3 4 7 |6 marks

Free notes are just the start.

Unlock every Workbook and Chapter at a Glance, and generate your own worksheets and predicted papers.

Explore plans

Related chapters

Types of numberSetsPowers and rootsFractions, decimals and percentagesOrderingThe four operations