Data Analysis, Statistics, and Probability
What to know
Candidates should read and interpret tables, bar graphs, line graphs, and circle graphs, and compute measures of center (mean, median, mode) and spread (range). Understand how outliers shift the mean more than the median. Probability basics include sample space, favorable outcomes over total outcomes, complementary events, and simple compound events. Distinguish experimental from theoretical probability and recognize misleading graphs.
Traps to watch
- The median requires data in order; with an even count, average the two middle values.
- An outlier pulls the mean toward it but barely moves the median.
- Probability is favorable outcomes divided by total equally likely outcomes-never favorable over unfavorable.
- For independent events, multiply probabilities; for either-or with no overlap, add them.
- Circle-graph percentages must total 100%; check whether a question asks for a count or a percent.
Worked example
Data: 3, 5, 5, 7, 20. Mean = 40 ÷ 5 = 8. Median = 5 (middle of the ordered list). Mode = 5. Range = 20 − 3 = 17. The value 20 is an outlier, so the median better represents the typical value.
Rule of thumb
Before computing, order the data and count the values. Ask whether the question wants a measure of center, a measure of spread, or a probability, and confirm whether the total is a count or a percentage.