Find the mean, median, mode, range and interquartile range of realistic fieldwork data. A new data set every time, with each step shown in the worked solution.
The rules
- Mean = total of the values ÷ number of values.
- Median = the middle value once the data is in order. Its position is (n + 1) ÷ 2. With an even number of values, take the midpoint of the two middle ones.
- Mode = the value that appears most often.
- Range = largest − smallest.
- Quartiles: with the data in order, the lower quartile is the value in position (n + 1) ÷ 4 and the upper quartile is the value in position 3(n + 1) ÷ 4.
- Interquartile range = upper quartile − lower quartile. It shows the spread of the middle half of the data and is not affected by extreme values.
- Mean from a frequency table = total of (frequency × value) ÷ total frequency. For grouped data, use the midpoint of each class: the answer is an estimate.
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