Statistics and probability
Ask for a mean, median, mode, a value read from a simple graph or table, or a simple probability written as a fraction.
Three "averages", three different questions
Mean, median and mode all try to describe a "typical" value, but they are calculated differently and can give different answers for the same data. Mean = add everything up, divide by how many there are. Median = put the data in order and find the middle value. Mode = whichever value appears most often.
Worked example: The data set is 2, 2, 5, 7, 9. Mean = (2 + 2 + 5 + 7 + 9) ÷ 5 = 5. Median (already in order) = 5, the middle value. Mode = 2, since it appears twice.
Probability as a fraction
Probability describes how likely something is, written as a fraction: (number of outcomes you want) ÷ (total number of possible outcomes). A probability of 0 means impossible; a probability of 1 means certain.
How to attack this question type
- 1
Order the data first before finding the median — this is the single most common source of errors in these questions.
- 2
Mean, median and mode can all be different numbers for the same data set. Read the question carefully to check which one is being asked for.
- 3
When reading a bar or column graph, check the scale on the axis first — each gridline might represent 2, 5 or 10 units, not always 1.
- 4
For probability, the denominator is the TOTAL number of possible outcomes, not just one of the categories — count everything in the bag, jar or spinner.
- 5
Always simplify your probability fraction, and sense-check it: it should always land between 0 and 1.
Practice · untimed
Five students scored 3, 5, 9, 9, 9 out of 10 on a pop quiz. What was the mean score?
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