Data Analysis, Statistics, and Probability
What Data Analysis, Statistics, and Probability covers
This domain tests reading tables, pictographs, bar graphs, and line graphs; calculating mean, median, mode, and range; and assigning simple probabilities. You need to interpret scales, compare data sets, and describe outcomes using fractions, decimals, or percentages between 0 and 1.
Core rules
- Read the scale: each gridline may stand for 2, 5, 10, or another interval; count the intervals, not the lines.
- Mean = sum of values ÷ number of values. Median = middle value after ordering; if there is an even number of values, average the two middle values. Mode = most frequent value. Range = highest − lowest.
- Probability of an event = number of favourable outcomes ÷ total equally likely outcomes. It lies from 0 to 1. P(not A) = 1 − P(A).
- In a bar graph, compare bar heights; in a line graph, describe change over time; in a pictograph, multiply the symbol value by the number of symbols.
- A sample space lists all possible outcomes; for two independent choices, multiply the number of options.
Worked example
Find the mean, median, mode, and range of 4, 7, 7, 9, 13. Sum = 40; there are 5 values, so mean = 40 ÷ 5 = 8. Ordered data: 4, 7, 7, 9, 13; median = 7. Mode = 7. Range = 13 − 4 = 9. If a bag has 3 red, 2 blue, and 5 green counters, P(red) = 3/10 = 0.3; P(not red) = 7/10 = 0.7.
Traps that cost marks
Finding the median without ordering the data first. Treating the mode as the middle rather than the most frequent. Reading a graph line as a value instead of using the scale. Giving probability as “3 out of 5” when the total is 10. Forgetting that probability cannot exceed 1. When a question says “at least,” include the boundary value; when it says “more than,” exclude it. Also check whether a graph’s vertical axis starts at zero, because a broken axis can make small differences look large.