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Primary 6 · Mathematics · Statistics

Comparing data displays

Interpret and compare different ways of displaying data, including side-by-side column graphs, and think critically about how data is presented in the media.

Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026. How we review

These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.

Learning goals

Learners will

  • Read and interpret side-by-side column graphs that compare two groups.
  • Compare different displays of data and decide which is most suitable.
  • Think critically about how data is presented in the media, including misleading scales and small samples.

Success looks like

  • I can read a side-by-side column graph and write statements comparing the two groups.
  • I can explain which type of display suits a set of data and why.
  • I can spot features that make a graph or claim misleading, such as an axis that does not start at zero.

The big idea

A side-by-side column graph compares two (or more) groups across the same categories. For each category, the columns for each group are drawn next to each other, in different colours. A legend shows which colour belongs to which group.

Here is a survey of favourite sports from two groups of 18 people:

  • Swimming: Group A 8, Group B 5
  • Soccer: Group A 6, Group B 9
  • Tennis: Group A 4, Group B 4

From a side-by-side graph of this data we can quickly see that swimming was most popular in Group A, soccer was most popular in Group B, and tennis was equally popular in both.

Different displays suit different purposes. A side-by-side column graph compares groups. A line graph shows change over time. A dot plot shows how numerical data is spread out. A table gives exact values. Choosing the right display makes the data easier to understand.

Graphs in advertisements and news stories are sometimes misleading, even when the numbers are correct. Watch out for:

  • A vertical axis that does not start at zero, which makes small differences look huge.
  • Uneven scales, or no scale at all.
  • Very small samples, such as “4 out of 5 people prefer it” when only 5 people were asked.
  • Comparing counts from groups of very different sizes instead of comparing fractions or percentages.

When you see data in the media, ask: Who collected it? How many were asked? Does the scale start at zero? Does the graph match the claim being made?

Worked examples

Reading a side-by-side column graph

Using the sports survey above (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), write three comparing statements.

  1. Compare the most popular sport in each group: swimming in Group A (8), soccer in Group B (9).
  2. Find a difference: Group B had 9 − 6 = 3 more people choose soccer than Group A.
  3. Look for a match: both groups had 4 people choose tennis.

Answer: Swimming was most popular in Group A, but soccer was most popular in Group B. Three more people in Group B chose soccer. Tennis was equally popular in both groups.

Spotting a misleading axis

A graph shows Brand A sold 95 bikes and Brand B sold 100 bikes. Its vertical axis starts at 90. Why is the graph misleading?

  1. Starting at 90, Brand A's column is 95 − 90 = 5 units tall and Brand B's is 100 − 90 = 10 units tall.
  2. So Brand B's column looks twice as tall as Brand A's.
  3. But the real difference is only 5 bikes out of about 100, which is small.

Answer: Because the axis does not start at zero, Brand B looks like it sold twice as many bikes, when it only sold 5 more.

Comparing groups of different sizes

At Club X, 30 of the 60 members walk to training. At Club Y, 40 of the 100 members walk. A poster says “More Club Y members walk.” Is that a fair comparison?

  1. Club Y has more walkers (40 compared with 30), but it also has more members.
  2. Compare fractions instead: Club X is 3060 = 12 = 50%. Club Y is 40100 = 40%.
  3. A greater share of Club X members walk.

Answer: The claim is true in numbers but misleading. A bigger share of Club X members walk (50% compared with 40%).

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.Favourite sports — Swimming: Group A 8, Group B 5; Soccer: Group A 6, Group B 9; Tennis: Group A 4, Group B 4. Which sport was most popular in Group B?
  2. 2.Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), how many people in Group A were surveyed?
  3. 3.Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), how many more people in Group B than in Group A chose soccer?
  4. 4.Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), which sport was equally popular in both groups?
  5. 5.A column graph's vertical axis starts at 90 instead of 0. What effect does this usually have?
  6. 6.An advertisement says “4 out of 5 people prefer our toothpaste”. Only 5 people were asked. What is the main problem with this claim?
  7. 7.In the sports survey, 8 of the 18 people in Group A chose swimming. What fraction of Group A chose swimming, in simplest form? (Type your answer like 1/2.)
  8. 8.Which display is best for comparing the favourite sports of two different groups?
Answer guide for parents

  1. Favourite sports — Swimming: Group A 8, Group B 5; Soccer: Group A 6, Group B 9; Tennis: Group A 4, Group B 4. Which sport was most popular in Group B?

    Soccer — In Group B, 9 people chose soccer, which is more than swimming (5) or tennis (4).

  2. Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), how many people in Group A were surveyed?

    18 — 8 + 6 + 4 = 18 people.

  3. Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), how many more people in Group B than in Group A chose soccer?

    3 — 9 − 6 = 3.

  4. Using the same survey (Swimming: A 8, B 5; Soccer: A 6, B 9; Tennis: A 4, B 4), which sport was equally popular in both groups?

    Tennis — Tennis was chosen by 4 people in each group.

  5. A column graph's vertical axis starts at 90 instead of 0. What effect does this usually have?

    It makes small differences look much bigger than they really are. — Cutting off the bottom of the columns exaggerates the differences in their heights.

  6. An advertisement says “4 out of 5 people prefer our toothpaste”. Only 5 people were asked. What is the main problem with this claim?

    The sample is too small to be reliable. — With only 5 people, the result could easily change a lot if different people were asked. Larger samples give more reliable results.

  7. In the sports survey, 8 of the 18 people in Group A chose swimming. What fraction of Group A chose swimming, in simplest form? (Type your answer like 1/2.)

    4/9 — 818: divide the numerator and denominator by 2 to get 49.

  8. Which display is best for comparing the favourite sports of two different groups?

    A side-by-side column graph — A side-by-side column graph shows both groups' results for each category next to each other, so they are easy to compare.

Watch out for

  • Comparing only the heights of columns without checking where the axis starts. Always read the scale before drawing conclusions.
  • Treating bigger counts as a bigger share when the groups are different sizes. Convert to fractions or percentages to compare fairly.
  • Believing a claim because it includes numbers. Encourage the learner to ask how many people were surveyed and who collected the data.

Tips for parents

  • Collect graphs and statistics from catalogues, news websites and advertisements and discuss together whether each one is fair.
  • Ask “What would this graph look like if the axis started at zero?” and sketch it together.
  • Let the learner draw the same data in two different ways and explain which one tells the story more honestly.

Go further

  • Survey two groups (for example, children and adults) about the same question, draw a side-by-side column graph and write five comparing statements.
  • Deliberately draw a misleading version of a fair graph by changing the scale, then explain the trick you used.
  • Find a claim in an advertisement that uses numbers, and write three questions you would want answered before you believed it.

About 45 minutes

Make a lesson planAssign to my child

You'll need

  • Grid paper, a ruler and two coloured pencils
  • Newspapers, magazines, catalogues or printed advertisements that include graphs or statistics
  • Paper and pencil

Key words

Side-by-side column graph
A column graph where the columns for two or more groups are drawn next to each other for each category, so they can be compared.
Legend
The part of a graph that shows which colour or pattern stands for each group.
Axis
One of the lines along the edge of a graph that shows the categories or the scale.
Sample
The group of people or things that data was collected from.
Misleading
Giving a wrong impression, even if the numbers themselves are true.
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