Data Handling and Probability
Data Handling and Probability tests interpretation as much as calculation: reading tables and graphs correctly, choosing the right average, and counting equally likely outcomes. Practice tasks can combine a small data set with a probability or expected-frequency question.
Core rules
- Mean = sum of values ÷ number of values. The median is the middle value after sorting; with an even count, average the two middle values. The mode is the most frequent value; the range is maximum minus minimum.
- A weighted mean uses the totals, not the average of the group means.
- Probability = favourable outcomes ÷ all equally likely outcomes. Probabilities lie from 0 to 1, and P(not A)=1−P(A).
- Expected frequency = probability × number of trials.
- For two events without replacement, the denominator changes after the first draw.
Worked example
A box contains 4 red and 6 white balls. Two balls are drawn without replacement. Find the probability that both are red. First draw: P(red)=4/10. If a red ball is removed, 3 red and 6 white remain, so the second draw has probability 3/9. Multiply: 4/10×3/9=12/90=2/15. The multiplication is valid because the second probability is conditional on the first result.
Traps
- Taking the median before sorting the data.
- Using denominator 10 again on a without-replacement second draw.
- Confusing at least one with exactly one.
- Reading a histogram bar height without checking the scale or class width.
- Reporting a probability greater than 1 after an arithmetic slip.