The mean is the sum of all values divided by the number of values; the median is the middle value after ordering the data; and the mode is the most frequent value. These are the three main measures of central tendency in IB Mathematics: Applications and Interpretation SL 4.3.
| Measure | Calculation | Important detail |
|---|---|---|
| Mean |
| Uses every data value |
| Median | Order the values and locate the middle | For an even number of values, average the two middle values |
| Mode | Identify the value with the greatest frequency | There may be one mode, multiple modes, or no mode |
Consider the data set:
For the mean, add the values and divide by :
The data are already ordered. The third value is in the middle, so the median is . The value appears most frequently, so the mode is also .
For data in a frequency table, calculate the mean using
where is each value and is its frequency. For grouped data, use each class midpoint for , so the resulting mean is an estimate rather than an exact value.
The appropriate measure depends on the distribution. The mean reflects every observation but can be strongly affected by an extreme value. The median is resistant to outliers, so it often represents skewed data better. The mode is useful for identifying the most common category or value, including non-numerical categorical data.
A common misconception is that the median can be found before ordering the data. This is incorrect: values must always be arranged from smallest to largest first. Another mistake is assuming every data set has exactly one mode.
Exam technique: This SL 4.3 skill may appear in a GDC-active Paper 1 short-response question or within a Paper 2 context. Show the mean calculation or GDC setup, use the population mean where required, and do not round intermediate values prematurely.
