Summarising Data: Mean, Median, Mode, Range

Four numbers summarise a data set:

• Mean (average): add all values, divide by how many there are.
• Median: the middle value once the data is put in order.
• Mode: the value that appears most often.
• Range: largest value minus smallest value (a measure of spread).

Worked example. Data: $4, 7, 7, 2, 10$. Ordered: $2, 4, 7, 7, 10$.

• Mean $= \dfrac{4+7+7+2+10}{5} = \dfrac{30}{5} = 6$.
• Median $= 7$ (the middle of five ordered values).
• Mode $= 7$ (it appears twice).
• Range $= 10 - 2 = 8$.

Exam checkpoint

Mean, median, mode and range each tell a different story. Mean shares the total equally; median is the middle value after ordering; mode is the most frequent value; range is highest minus lowest. Choose the measure that answers the question and check whether an outlier makes the mean misleading.

Short worked example. For $3,5,5,7,10$, mean $=30\div5=6$, median $=5$, mode $=5$, range $=10-3=7$.