Statistics and Probability / Data Handling - Grade 6 Numeracy
Statistics and Probability tests how you collect, display, describe, and interpret data, and how you reason about chance. Questions may ask you to choose a graph, calculate mean, median, mode, or range, read scales carefully, or find a probability from equally likely outcomes.
Core rules
- A graph should match the data: bar graphs compare categories, line graphs show change over time, and circle graphs show parts of a whole.
- Mean = sum of values ÷ number of values. Median = middle value after ordering. Mode = most frequent value. Range = maximum − minimum.
- The mean is affected by outliers; the median is often more representative when one value is unusually high or low.
- Read graph scales, labels, and intervals carefully; a broken axis can make small differences look large.
- Probability measures how likely an event is, from 0 (impossible) to 1 (certain). For equally likely outcomes, P(event) = favourable outcomes ÷ total outcomes.
- List the sample space to avoid missing outcomes; probability can be written as a fraction, decimal, or percent.
- Experimental probability comes from results you actually collect; theoretical probability comes from analysing equally likely outcomes.
Worked example
Quiz scores: 4, 7, 7, 9, 13. Mean: (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8. Median: order the values (already ordered); the middle value is 7. Mode: 7 appears twice, more than any other value. Range: 13 − 4 = 9. Reasoning: The mean is pulled upward by 13, while the median and mode stay at 7. For a typical score, the median is more representative here.
Traps that cost marks
- Finding the median without ordering the data first.
- Calling the range a measure of centre; it describes spread.
- Using the total number of outcomes as the numerator in a probability.
- Assuming the most frequent outcome is certain.
- Ignoring a graph’s scale or labels.
- Treating experimental probability as a guarantee rather than an estimate.