Statistics and Probability
Core ideas
This domain covers summarising data and quantifying chance. You need mean, median, mode and range from raw data and from frequency tables; reading and interpreting graphs; the probability scale from 0 to 1; theoretical versus experimental probability; complementary events; combined events using lists, tables and tree diagrams; and the difference between independent and mutually exclusive events.
Traps
- Finding the median without first ordering the data.
- With an even number of values, quoting one middle value instead of the mean of the two middle values.
- Choosing the mean when an outlier makes the median a better summary.
- Ignoring the total frequency when calculating a mean from a frequency table.
- Adding probabilities for independent events when they should be multiplied.
Worked example
A fair coin is tossed twice. Find the probability of at least one head. Use the complement: P(no heads) = P(tail, tail) = ½ × ½ = ¼. Therefore P(at least one head) = 1 - ¼ = ¾.
Rule of thumb
P(not A) = 1 - P(A). Whenever a question says 'at least one', check whether the complement is quicker to compute - it usually is, and it avoids listing every favourable outcome.