Statistics and Probability
Statistics and Probability tests how data are collected, organised, summarised and interpreted, and how likely events are quantified. You need to read tables and charts, calculate averages and spread, construct simple probability spaces, and make sensible comments about what the data show.
Core rules and concepts
- Mean = sum of values ÷ number of values. For a frequency table, mean = Σ(fx) ÷ Σf.
- Median: arrange values in order; the median is the middle value, or the mean of the two middle values for an even count.
- Mode is the most frequent value or class; range = largest value − smallest value.
- Pie charts: angle for a category = (frequency ÷ total) × 360°.
- Probability is between 0 and 1. P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
- P(not A) = 1 − P(A).
- For two independent events, multiply their probabilities; for mutually exclusive events, add them.
Worked example
A bag has 5 red, 3 blue and 2 green counters. One counter is taken at random. Total counters = 5 + 3 + 2 = 10. P(red) = 5/10 = 1/2. P(not blue) = 1 − 3/10 = 7/10. P(red or green) = 5/10 + 2/10 = 7/10, because these outcomes cannot happen together.
Traps that cost marks
Finding the median without ordering the data; dividing by the wrong total in a frequency table; writing a probability greater than 1; adding probabilities for independent events when multiplication is required; and reading a bar chart’s height without checking the scale.