The Cartesian Plane, Data and Probability: Year 6 Study Guide
Graphs and probability help us make sense of information and uncertainty.
The Cartesian plane has a horizontal x-axis and a vertical y-axis that meet at the origin (0, 0). Points are written as (x, y), where x is the horizontal and y the vertical position. All four quadrants are used in Year 6, with negative values to the left of and below the origin.
In Statistics, students collect and organise data, display it in graphs (column, line, dot plot, stem-and-leaf) and calculate the mean (the average), median (the middle) and mode (the most common).
Mean, median, mode and range
For the data 3, 5, 5, 6, 9: the mode is 5, the median is 5 (the middle value), the mean is (3 + 5 + 5 + 6 + 9) ÷ 5 = 5.6 and the range is 9 − 3 = 6. For an even number of values, the median is halfway between the two middle values.
| Measure | How to find it | Data 3, 5, 5, 6, 9 |
|---|---|---|
| Mode | most frequent | 5 |
| Median | middle value | 5 |
| Mean | total ÷ count | 5.6 |
| Range | highest − lowest | 6 |
Reading graphs
Check the title, the axes and the scale. A line graph shows change over time; a column graph compares categories; a dot plot shows frequency. Ask: What is the highest? What is the trend? Is the scale starting at zero? A graph with a broken scale can make a small difference look big.
What is it about?
Units and intervals.
High, low, trend.
Support it with numbers.
Probability
Probability is the chance of an event, from 0 (impossible) to 1 (certain). Equally likely outcomes: P(event) = favourable outcomes ÷ total outcomes. The chance of rolling an even number on a die is 3/6 = 1/2 = 0.5 = 50%. Compare theoretical probability with experimental results. Run many trials; results come closer to the expected value.
Worked examples and common mistakes
Example: A spinner with 8 equal sections has 3 red: P(red) = 3/8. Common mistakes: mixing up median and mean, forgetting to order data before finding the median and giving the coordinates in the wrong order. Always write (across, up).
Check your understanding: model answers
1. Ordered: 2, 4, 6, 8, 10, so the median is 6. 2. The top-left quadrant. 3. 1/6.
✨ Key Takeaways
- Coordinates: (x, y), across then up.
- Mean, median and mode describe data.
- Probability is between 0 and 1.
- Read the scale of a graph carefully.
💬 Questions for Discussion & Reflection
- Find the median of 2, 8, 4, 10, 6.
- Which quadrant holds (−3, 4)?
- What is P(rolling a 5) on a fair die?
Print coordinate plane grids →