Statistics and Probability - Te Tatauranga me te Tūponotanga
Statistics and probability questions ask you to describe data, choose and read displays, calculate summary values, and assign or interpret probabilities and risk.
Core rules and concepts
- Data is categorical (categories such as colours) or numerical (discrete counts or continuous measurements). Choose displays to suit: bar charts for categories, histograms for continuous data, scatter plots for two numerical variables.
- Mean = sum of values ÷ number of values. Median is the middle value of ordered data; mode is the most frequent. Range = maximum − minimum.
- The mean is affected by outliers; the median is resistant. Report which is more representative and why.
- Probability of an event = number of favourable outcomes ÷ total equally likely outcomes. It lies from 0 to 1. The complement rule is P(not A) = 1 − P(A).
- For independent events, multiply probabilities. For mutually exclusive events, add probabilities.
- Risk can be expressed as a fraction, decimal, percentage or “1 in n”; compare risks using the same format.
Worked example
Six test scores are 12, 15, 15, 18, 20 and 60. Mean = (12 + 15 + 15 + 18 + 20 + 60) ÷ 6 = 140 ÷ 6 = 23.3 (1 dp). Ordered data: 12, 15, 15, 18, 20, 60. Median = (15 + 18) ÷ 2 = 16.5. Mode = 15. The score 60 is an outlier and pulls the mean above most scores, so the median 16.5 is a better typical value. The probability of choosing a 15 at random is 2/6 = 1/3.
Traps
- Finding the median without ordering the data first.
- Reading a graph without checking the axis scale or whether it starts at zero.
- Treating correlation as proof of causation.
- Adding probabilities of independent events instead of multiplying, or forgetting the complement for “at least one”.