Statistics and Probability
What the domain tests
This domain covers collecting and organising data, reading and drawing diagrams, calculating averages, and finding simple probabilities. Typical exam items give a frequency table or a diagram and ask you to compute and then interpret - for example to say which average best describes the data.
Core rules
- Diagrams: a bar chart compares categories, a line chart shows change over time, a histogram groups numerical data into classes, and a pie chart shows parts of a whole, with each sector angle equal to (frequency/total)·360°.
- Mean: add all values and divide by how many there are. For a frequency table use the weighted mean, (Σ f·x)/(Σ f).
- Median: order the data first; with an odd count it is the middle value, with an even count it is the mean of the two middle values.
- Mode: the most frequent value; there may be several or none.
- Range: maximum minus minimum, a measure of spread only.
- Choosing an average: the mean uses every value and is pulled strongly by an outlier; the median resists outliers; the mode suits non-numerical categories such as shoe size or favourite subject.
- Probability: for equally likely outcomes P(A) = number of favourable outcomes / total number of outcomes, always between 0 and 1. P(not A) = 1 − P(A). Relative frequency from an experiment approaches the theoretical probability as the number of trials grows.
Worked example
Test scores: 4, 7, 7, 9, 10, 7, 5. Sum = 49 and there are 7 scores, so the mean is 7. Ordered: 4, 5, 7, 7, 7, 9, 10 - the median is the fourth value, 7. The mode is 7, the most frequent score, and the range is 10 − 4 = 6. Probability check: a bag holds 3 red, 5 blue and 2 green balls, 10 in total. P(blue) = 5/10 = 0,5, so P(not blue) = 1 − 0,5 = 0,5, that is 5 out of 10.
Traps that cost marks
- Finding the median without sorting the data first.
- Forgetting to average the two middle values when the count is even.
- Dividing by the number of different values instead of the number of data points in a weighted mean.
- Reporting the range as an average, or the mode as a measure of spread.
- Giving a probability greater than 1, or forgetting that all outcomes must be equally likely for the simple formula to apply.