Measurement, Space & Statistics
Interpreting Data and Understanding Probability
Year 5 · Year 6
- ✓Interpret information presented in various data displays, including tables, column graphs, dot plots, and simple sector graphs.
- ✓Compare and draw conclusions from different data representations.
- ✓Use the language of chance to describe the likelihood of everyday events.
- ✓Order events from least likely to most likely.
- ✓Express the probability of simple events as fractions.
Key concepts
Data displays are visual ways to show information (data) so it's easy to understand and compare. Common types include tables, column graphs, dot plots, and simple sector graphs (sometimes called pie charts). It's important to always look for the key features of any data display to understand the information correctly.
When looking at a data display, always check for these important parts:\n- Title: Tells you what the graph or table is about.\n- Labels: Explain what each axis (on a graph) or column/row (in a table) represents.\n- Scale: The numbers used on the axes of a graph, showing how the data is measured.\n- Key: Explains any symbols, colours, or patterns used in the display (e.g., in a picture graph or sector graph).
Interpreting data means reading and understanding the information shown in a data display. This involves:\n- Finding specific values or amounts.\n- Comparing different categories or groups.\n- Identifying the most popular, least popular, or most frequent items.\n- Drawing simple conclusions or making statements about the data.
Probability is a measure of how likely an event is to happen. We use special words to describe the chance of an event occurring. Understanding probability helps us make predictions about future events.
We use specific words to describe the likelihood of an event:\n- Impossible: Will never happen (e.g., a fish flying).\n- Unlikely: Has a small chance of happening (e.g., winning a major lottery).\n- Equally likely: Has an even chance of happening (e.g., flipping a coin and getting heads).\n- Likely: Has a good chance of happening (e.g., it being sunny in summer).\n- Certain: Will definitely happen (e.g., the sun rising tomorrow).
For events where all possible outcomes are equally likely, we can express the probability as a fraction. This fraction tells us the proportion of times we expect a particular event to happen out of all possible outcomes.
Key facts to remember
- 1Data displays help us understand information quickly and clearly.
- 2Always check the title, labels, scale, and key of any data display before interpreting it.
- 3Interpreting data involves reading, comparing, and drawing conclusions from the information presented.
- 4Probability tells us how likely an event is to happen.
- 5The language of chance (impossible, unlikely, equally likely, likely, certain) helps us describe probabilities.
- 6Probability can be expressed as a fraction: (Number of favourable outcomes) / (Total number of possible outcomes).
- 7A probability of 0 means an event is impossible, and a probability of 1 means an event is certain.
Worked examples
Example 1
The column graph below shows the favourite colours of students in Year 6. Use the graph to answer the questions.\n\n[Imagine a column graph with 'Favourite Colour' on the x-axis (Red, Blue, Green, Yellow, Purple) and 'Number of Students' on the y-axis (0 to 10, in steps of 2).]\n\nData points:\nRed: 8 students\nBlue: 10 students\nGreen: 4 students\nYellow: 6 students\nPurple: 2 students\n\na) Which colour is the most popular?\nb) How many students chose Yellow?\nc) How many more students chose Red than Green?\nd) How many students were surveyed in total?
Answer
a) Blue\nb) 6 students\nc) 4 more students\nd) 30 students
Always check the scale on the y-axis carefully when reading the number of students.
Example 2
Order the following events from least likely to most likely:\n\nA. Rolling a standard six-sided die and getting a 9.\nB. Flipping a fair coin and getting tails.\nC. Picking a blue marble from a bag containing 1 red, 1 green, and 1 blue marble.\nD. The sun rising in the east tomorrow morning.
Answer
A (Impossible), C (Equally likely), B (Equally likely), D (Certain)\n(Note: C and B can be swapped as they are both 'equally likely'.)
Think about the real-world chance of each event happening.
Example 3
A bag contains 4 red, 3 blue, and 5 green counters. If you pick one counter from the bag without looking, what is the probability of picking a blue counter? Express your answer as a fraction.
Answer
The probability of picking a blue counter is 1/4.
Always simplify fractions to their simplest form in your final answer.
Common mistakes
- ✗Misreading the scale on a graph, especially if it doesn't start at zero or uses intervals other than one.
- ✗Ignoring the key on a picture graph or sector graph, leading to incorrect counts.
- ✗Confusing 'likely' with 'certain' or 'unlikely' with 'impossible' when describing chance.
- ✗Not considering all possible outcomes when calculating probability, leading to an incorrect total.
- ✗Not simplifying fractions for probability answers to their simplest form.
Exam tips
- ★Read all graph titles, labels, and keys very carefully before attempting to answer any questions.
- ★Use a ruler to help you accurately read values from scales on column graphs or dot plots.
- ★When ordering events by likelihood, think about what you know about the real world and the specific conditions given.
- ★For probability questions, always list all possible outcomes first to ensure your total is correct.
- ★Double-check your calculations, especially when adding up totals or simplifying fractions.
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