Mean, median and mode

Statistical techniques summarise data so we can understand it without reading every value. A measure of central tendency is one value that gives an idea of the whole data. The three most common are the mean, median and mode.

Mean (average) = sum of the values ÷ number of values. For the book's nine student heights (cm) 90, 102, 110, 115, 85, 90, 100, 110, 110, the sum is 912, so the mean is 912 ÷ 9 = 101.33 cm.

• An outlier is an exceptionally large or small value compared with the rest. Outliers pull the mean, so the mean is not suitable when there are outliers; the book suggests removing them first.

Median: sort the values (ascending or descending) and take the middle one.

• With an odd number of values, it is the value in the middle position: the sorted heights are 85, 90, 90, 100, 102, 110, 110, 110, 115, so the median is the 5th value, 102 cm.
• With an even number of values, it is the average of the two middle values.
• The median divides the data into two equal halves.

Mode: the value that appears most often. For the heights it is 110 cm (three times).

• A data set has no mode if every value appears once, and can have several modes if more than one value shares the highest frequency.
• The mode works for non-numeric data too (for example, the most common colour).

Example (new): for a cricketer's scores 12, 45, 45, 30, 8, the mean is 140 ÷ 5 = 28; sorted, 8, 12, 30, 45, 45, the median is 30; and the mode is 45. If one more innings of 200 is added, the mean jumps to 340 ÷ 6, about 56.7, while the median moves only to (30 + 45) ÷ 2 = 37.5: the outlier pulls the mean far more.