Statistics and Probability
Statistics and probability tests mean, median, mode, range, and simple probability. SEE data questions may use individual observations or a frequency table; probability questions use bags, cards, dice, or spinners, and sometimes the complement rule.
Core rules
- Mean = sum of observations ÷ number of observations. For a frequency table, mean = Σfx/Σf.
- Median: arrange in order. For odd n, take the middle value; for even n, average the two middle values.
- Mode is the most frequent value; a data set can have no mode or more than one mode.
- Range = largest value − smallest value.
- Probability P(E)=number of favourable outcomes ÷ total equally likely outcomes; 0≤P(E)≤1; P(not E)=1−P(E).
- For two independent events, P(A and B)=P(A)×P(B); for mutually exclusive events, P(A or B)=P(A)+P(B).
Worked example
The data 4, 7, 7, 9, 13 have sum 40 and n=5, so mean=8. In order, the median is the third value, 7. The mode is 7 because it appears twice. Range=13−4=9. A bag has 5 red and 3 blue balls; P(red)=5/8, so P(not red)=1−5/8=3/8. If two balls are drawn without replacement, the second denominator becomes 7.
Traps
- Finding the median without sorting the data.
- For even n, choosing one middle value instead of averaging both.
- Saying “no mode” when a value repeats, or missing a tie for mode.
- Using total outcomes that are not equally likely.
- Forgetting to reduce the denominator after a without-replacement draw.