Data, Statistics and Chance
What you need to understand
This domain covers collecting, displaying and interpreting data, and reasoning about chance. You should know the difference between categorical and numerical data, and between discrete and continuous data. You need to read and compare tables, bar charts, line graphs, pie charts and stem-and-leaf plots, and to calculate and interpret mean, median, mode and range. You should understand that the mean is affected by outliers while the median is not, and be able to choose which average best describes a data set. For chance, you should be able to list outcomes, use simple probability as favourable outcomes over total outcomes, and recognise that probabilities range from 0 to 1.
Traps to watch for
- Misleading graphs. A broken axis or uneven scale can exaggerate differences.
- Mean versus median. One very large value can pull the mean far above the median.
- Pie chart angles. Each category's angle is its fraction of the total multiplied by 360°.
- Independent events. The probability of two independent events both happening is the product of their probabilities.
- Sample size. Small samples can produce unreliable conclusions.
Worked example
A student scores 60, 65, 70, 75 and 100 on five tests. Mean = 370 ÷ 5 = 74. Median = 70 (the middle value when ordered). The score of 100 pulls the mean above the median, so the median better represents a typical result.
Rule of thumb
Order the data first, then find the median; check whether an outlier is distorting the mean.