What are measures of central tendency?
A measure of central tendency is a single value that represents the centre of a set of data. The three most common measures are the mean, the median and the mode. Each one tells us something different about where the data is grouped.
Key idea / Key idea
Mean = (sum of all values) ÷ (number of values). Median = the middle value after the data is arranged in order. Mode = the value that appears most often.
Finding each measure
To find the mean, add every value and divide by how many values there are. To find the median, first arrange the data from smallest to largest. If there is an odd number of values, the median is the middle one. If there is an even number of values, the median is the average of the two middle values. The mode is simply the value with the highest frequency; a set may have one mode, more than one mode, or no mode at all.
Worked example
Find the mean, median and mode of: 5, 8, 8, 6, 3.
Mean = (5 + 8 + 8 + 6 + 3) ÷ 5 = 30 ÷ 5 = 6.
Median: arrange as 3, 5, 6, 8, 8. The middle value is 6, so median = 6.
Mode: 8 appears twice, more than any other value, so mode = 8.
Choosing a measure
The mean uses every value, so it is affected by very large or very small values (extreme values). The median is not affected by extreme values, so it is useful when the data has outliers. The mode is helpful for non-numerical data, such as the most popular colour.
Remember
- Always arrange data in order before finding the median.
- For an even number of values, average the two middle numbers.
- The mean can be a decimal even if all the data are whole numbers.