Practice Maths

L47 — Types of Data Displays

Key Ideas

Key Terms

categorical data
Data that falls into named groups or categories, with no numerical order. Examples: favourite colour, type of pet, eye colour.
continuous data
Data that is measured and can take any value within a range. Examples: temperature, height, time.
bar/column graph
A display using rectangles (bars) to compare amounts across different categories. Vertical bars = column graph; horizontal bars = bar graph.
line graph
A display where data points are plotted and connected by a line. Used to show how a value changes over time.
pie chart
A circular display divided into sectors. Each sector represents a proportion of the whole, and all sectors add to 100%.
dot plot
A display where each data value is shown as a dot above a number line. Best suited to small datasets with individual values.
stem-and-leaf plot
A display that groups data by place value, keeping actual values visible while showing the distribution. The stem is the leading digit(s) and the leaves are the last digits.

Choosing the Right Display

Different types of data need different displays. Here are the most common:

  • Column/Bar graph: Used for categorical data (data in named groups, e.g. favourite sport, eye colour). Bars can be horizontal or vertical.
  • Line graph: Used for continuous data over time (e.g. temperature each hour, plant height each week). Shows trends and changes.
  • Pie chart: Used to show proportions — how parts relate to the whole (e.g. how 100 students are split across subjects).
  • Dot plot: Used for small datasets with individual values shown as dots on a number line. Easy to see frequency.
  • Stem-and-leaf plot: Shows the numerical distribution of a dataset while keeping the actual values visible.

Always check: title, axis labels, and scale before reading any graph.

Hot Tip: Always check the scale on the axis before reading values — it may not start at 0! A graph with a y-axis starting at 50 can make small differences look huge.

Worked Example

What display best suits each dataset?

Dataset 1: "Number of students who prefer each sport" (categories: Football, Basketball, Tennis, Swimming)

Answer: Bar/column graph — the data is categorical (named groups, not numbers on a scale). Each bar represents one category.

Dataset 2: "Temperature recorded each hour from 6am to 6pm"

Answer: Line graph — temperature is continuous data measured over time. A line graph shows the trend and how it changes hour by hour.

Why Do We Use Graphs?

When you collect data — like how many students chose each lunch option, or the temperature each day for a week — a list of numbers can be hard to make sense of. Graphs and charts turn those numbers into a picture, so patterns and differences jump out straight away. Different types of graphs suit different types of data, so knowing which one to choose is an important skill.

Column Graphs and Bar Graphs

Column graphs use vertical bars (up and down) and bar graphs use horizontal bars (side to side). Both do the same job: they compare amounts across different categories. For example, a column graph is perfect for showing how many students chose each favourite sport. The taller the bar, the bigger the value. Use these when your categories are separate (not continuous) — like types of pets, colours of cars, or days of the week.

Every good column or bar graph needs: a title, labelled axes (with units if needed), and evenly spaced bars of equal width.

Favourite Fruit — Column Graph Example 0 5 10 15 Number of students Apple Banana Mango Orange Fruit type Key features: title, labelled axes, uniform bar widths, scale starting at 0

Line Graphs

Line graphs are used when data changes over time. You plot points and connect them with straight lines. For example, showing how the temperature changes every hour through the day, or how your score improves across five tests. The horizontal axis (x-axis) almost always shows time. Line graphs are great for spotting trends — is the value going up, going down, or staying steady?

Test Score Over 5 Weeks — Line Graph Example 50 60 70 80 Score (%) Wk 1 Wk 2 Wk 3 Wk 4 Wk 5 Week Key features: x-axis shows time, connected points show the trend (rising here)

Pie Charts and Pictographs

A pie chart is a circle divided into slices. Each slice represents a category, and its size shows its proportion of the whole. Pie charts work best when you want to show how a total is divided up — for example, what fraction of students travel to school by bus, car, or on foot. All slices must add up to 100%.

Pictographs use small pictures or symbols to represent data. Each symbol stands for a certain number of items — this is shown in a key. For example, one apple symbol might represent 5 students. Pictographs are eye-catching but less precise than other graph types, especially if values don't divide evenly into whole symbols.

Favourite Sport — Pie Chart Example Football 25% Swimming 25% Basketball 50% Football (25%) Swimming (25%) Basketball (50%) All sectors add to 100%

Key features: sectors show proportions, all sectors must add to 100%, each sector is labelled with its category and percentage.

Dot Plots

A dot plot shows individual data values as dots above a number line. Each dot represents one value from the dataset. When two values are the same, dots are stacked vertically. Dot plots are best for small datasets — they make it easy to see the most common value (the tallest stack), the range (lowest to highest), and any gaps in the data.

Hours of Screen Time — Dot Plot Example 1 2 3 4 5 6 7 Hours per day

Key features: each dot = one value, stacked dots show repeated values, the tallest stack is the mode (4 hours here), the number line shows the scale.

Stem-and-Leaf Plots

A stem-and-leaf plot organises numbers by splitting each value into a stem (the leading digit or digits) and a leaf (the last digit). The stems are listed vertically and each leaf is written beside its stem. This keeps the actual data values visible while showing the shape of the distribution. Leaves must always be written in ascending order.

Stem-and-Leaf Plot Example
Key: 2 | 3 = 23
Stem|Leaves
1|2   5   8
2|1   3   3   7   9
3|0   4   6
4|2

Stem = tens digit (1 = 10s, 2 = 20s, etc.)

Leaf = units digit (e.g. stem 2, leaf 3 = 23)

Leaves always in order (smallest to largest)

Values shown: 12, 15, 18, 21, 23, 23, 27, 29, 30, 34, 36, 42

Choosing the Right Display

Ask yourself two questions: (1) What type of data do I have? (2) What am I trying to show? Use a column or bar graph to compare categories. Use a line graph to show change over time. Use a pie chart to show proportions of a whole. Use a pictograph when you want something visual and values are easy to represent with symbols. There is no single “best” graph — it depends on what story you want the data to tell.

Common mistake: Don't use a line graph for categories that have no natural order or time connection. For example, connecting "cats, dogs, fish, birds" with a line doesn't make sense — use a column or bar graph instead. Also, always check whether a graph's y-axis starts at 0. If it starts at a higher number, differences between bars can look much bigger than they really are.

  1. Match Data to Display

    For each dataset below, name the most appropriate display (bar graph, line graph, pie chart, dot plot, or stem-and-leaf plot).

    1. The number of goals scored by 10 different soccer players in a season (small dataset, values 0–8)
    2. The favourite colour of students in a Year 7 class
    3. The temperature in a city measured every day for a month
    4. The percentage of a school budget spent on different areas (sports, staffing, resources, excursions)
    5. The heights (in cm) of 20 students, ranging from 140 cm to 175 cm
    6. The number of books read by each student in a class of 8 over a term
    7. How a family spends their weekly income across five categories
    8. The monthly rainfall totals over one year

  2. Reading Values from Graphs

    Use the information from each described graph to answer the questions.

    Graph A — Column graph: "Students absent each day"

    DayMonTueWedThuFri
    Absences12815911
    Students Absent Each Day 0 4 8 12 16 Absences Mon Tue Wed Thu Fri Day
    1. Which day had the most absences?
    2. Which day had the fewest absences?
    3. What is the total number of absences for the week?
    4. How many more absences were there on Wednesday than Tuesday?

    Graph B — Line graph: "Plant height (cm) over 6 weeks"

    Week123456
    Height (cm)4711141418
    Plant Height (cm) Over 6 Weeks 0 5 10 15 20 Height (cm) Wk 1 Wk 2 Wk 3 Wk 4 Wk 5 Wk 6 Week
    1. How tall was the plant at the end of Week 3?
    2. Between which two consecutive weeks did the plant grow the most?
    3. During which week did the plant not grow at all?
    4. What was the total growth from Week 1 to Week 6?

    Graph C — Dot plot: "Number of pets owned by each student" (12 students)

    Values: 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 5

    Number of Pets Owned (12 Students) 0 1 2 3 4 5 Number of pets
    1. How many students own exactly 2 pets?
    2. What is the most common number of pets owned?
    3. How many students own 3 or more pets?
    4. What is the range of values in this dataset?

  3. Why Does the Display Choice Matter?

    1. Explain why a line graph is suitable for showing temperature recorded each hour, but would not be appropriate for showing favourite colours of students.
    2. A graph about school canteen sales shows the y-axis starting at 80 (not 0). The bar for "sandwiches" reaches 95 and the bar for "pies" reaches 88. A student says "sandwiches outsell pies by nearly double!" Is this claim correct? Explain what feature of the graph is misleading.
    3. Two students are comparing their test results over a semester. One wants to use a pie chart. Explain why a line graph would be more useful for this purpose.
    4. What must every good graph include? Name at least three features.

  4. Choose, Justify & Interpret

    1. A researcher has data on the number of hours of sleep 25 teenagers get each night (values ranging from 5 to 10 hours). Should they use a dot plot or a stem-and-leaf plot? Justify your answer.
    2. A school wants to show parents how the library budget is split between books, digital resources, furniture, and events. Which display would communicate this most clearly? Explain why.
    3. Two students each create a graph of the same data about daily step counts over 2 weeks. Student A uses a line graph; Student B uses a bar graph. Which is more appropriate and why?
    4. Look at this data: "Daily ice cream sales at a beach kiosk over summer: Jan avg = 120, Feb avg = 145, Mar avg = 95, Apr avg = 60." A bar graph is drawn with the y-axis starting at 50. Write one sentence describing what a reader might wrongly conclude, and one sentence about what the data actually shows.

  5. Identify the display type

    For each description, identify which type of graph is being described.

    1. A circular graph divided into sectors, each representing a proportion of the whole.
    2. A graph where each data value is shown as a dot above a number line.
    3. A graph where data values are written with their tens digit on the left and units digit as leaves on the right.
    4. A graph using rectangles to compare categories — the height shows frequency or amount.
    5. A graph showing how a value changes over time, with points connected by a line.
    6. A graph where two sets of data share the same central stem, with one group's leaves going left and the other going right.

  6. Describe what each graph shows

    Use the data table below to answer the questions.

    Favourite school subject — Year 7 class of 30 students:

    SubjectMathsEnglishSciencePEArt
    Students85764
    1. Which subject is most popular? Which is least popular?
    2. What percentage of students chose Maths? (Round to 1 decimal place.)
    3. Would a bar graph or pie chart be more suitable? Explain your choice.
    4. Would a line graph be appropriate here? Why or why not?

  7. Graph features and scale

    1. Use the column graph below to answer: How many students does the tallest bar represent?

      Students Who Play Each Sport 0 10 20 30 Number of students Football Basketball Tennis Swimming Athletics Sport

    2. Use the line graph below to answer: By how much did the temperature increase from Monday to Friday?

      Daily Temperature (°C) 15 20 25 30 35 Temp (°C) Mon Tue Wed Thu Fri Day
    3. A student draws a graph without a title or axis labels. Explain two problems this causes for someone reading the graph.

    4. Use the pie chart below to answer: What fraction of students use neither walking nor the bus to get to school?

      How Students Travel to School Bus 50% Walk 25% Other 25% Bus (50%) Walk (25%) Other (25%)

  8. Comparing and selecting displays

    1. A journalist wants to show how Queensland's average annual rainfall has changed over the past 20 years. Which display type would be most effective? Justify your answer with two reasons.
    2. A supermarket wants to compare the popularity of five breakfast cereal brands. Name one display that would work well and one that would not. For each, explain why.
    3. A class survey finds that students own between 0 and 6 pets each, with most owning 1 or 2. There are 15 students. Should you use a dot plot or a bar graph? What are the advantages of your chosen display for this dataset?
    4. Two displays are drawn using the same data about the number of hours students study per week: one is a dot plot and the other is a stem-and-leaf plot. What can you see clearly in one display that is harder to see in the other? Which would you choose if you needed to quickly find the median?

  9. Reading a pie chart

    A class of 40 students was asked how they travel to school. The results are shown in the table and pie chart below.

    MethodBusWalkCarBike
    Percentage40%25%30%5%
    Travel to School (40 Students) Bus 40% Walk 25% Car 30% Bus (40%) Walk (25%) Car (30%) Bike (5%)
    1. How many students travel by bus?
    2. How many students walk to school?
    3. What is the most common travel method?
    4. How many more students travel by car than by bike?
    5. Do all percentages add to 100%? Check your work.

  10. Real-world data investigation

    1. A sports coach records a player's sprint times (seconds) over 8 training sessions: 12.4, 12.1, 11.9, 11.7, 11.8, 11.5, 11.4, 11.2. Which type of graph best shows whether the player is improving? Sketch the axes you would use and label them.
    2. The same sprint times are used to make a dot plot. What would the dot plot show that the line graph does not? Give one advantage and one disadvantage of the dot plot for this data.
    3. A council records the types of rubbish found on a beach cleanup: plastic 45%, glass 20%, metal 15%, paper 12%, other 8%. A bar graph is drawn. Describe what the y-axis should show and what scale would be appropriate.
    4. You are designing a display for a school report showing how 60 students rated a new canteen menu (ratings: 1, 2, 3, 4, or 5 stars). Suggest a suitable graph type and explain what information it would highlight to the reader.
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