Handling Data
This domain covers collecting, summarising and interpreting data, and basic probability. SEC questions include frequency tables, charts, averages, cumulative frequency, scatter graphs and probability trees. Marks are given for showing the calculation, so write the sum, not just the mean.
Averages and displays
- Mean = total of values ÷ number of values; from a frequency table, mean = Σfx ÷ Σf.
- Median: order the data; for n values the median is the ((n + 1)/2)th value.
- Mode = most frequent value; range = largest − smallest.
- Grouped data: the modal class has the highest frequency; estimate the mean using class midpoints.
- Cumulative frequency: plot at upper class boundaries; median at n/2, quartiles at n/4 and 3n/4; interquartile range = UQ − LQ.
- Scatter graphs: describe correlation as positive, negative or none, and distinguish correlation from causation.
Probability
- P(event) = favourable outcomes ÷ total outcomes; 0 ≤ P ≤ 1; P(not A) = 1 − P(A).
- Mutually exclusive events: add probabilities.
- Independent events: multiply probabilities.
- Tree diagrams: multiply along branches and add between branches.
- Relative frequency = number of successes ÷ number of trials.
Worked example
A bag has 5 red and 3 blue counters. Two are taken without replacement. Find P(both red). First draw: P(red) = 5/8. After removing one red, 4 red and 3 blue remain, so the second draw has P(red) = 4/7. Therefore P(both red) = 5/8 × 4/7 = 20/56 = 5/14.
Traps
- Using the original total on the second draw in a without-replacement question.
- Adding probabilities along a tree branch instead of multiplying.
- Reading a cumulative frequency graph at a class midpoint rather than the upper boundary.
- Treating the mean of grouped data as exact-it is an estimate.