# Measures of Central Tendency

Measures of Central Tendency provide a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution. There are three main measures of central tendency: the mean, the median and the mode.

When data is normally distributed, the mean, median and mode should be identical, and are all effective in showing the most typical value of a data set.

It's important to look the dispersion of a data set when interpreting the measures of central tendency.

### Mean

The mean of a data set is also known as the average value. It is calculated by dividing the sum of all values in a data set by the number of values.

So in a data set of 1, 2, 3, 4, 5, we would calculate the mean by adding the values (1+2+3+4+5) and dividing by the total number of values (5). Our mean then is 15/5, which equals 3.

Disadvantages to the mean as a measure of central tendency are that it is highly susceptible to outliers (observations which are markedly distant from the bulk of observations in a data set), and that it is not appropriate to use when the data is skewed, rather than being of a normal distribution.

### Median

The median of a data set is the value that is at the middle of a data set arranged from smallest to largest.

In the data set 1, 2, 3, 4, 5, the median is 3.

In a data set with an even number of observations, the median is calculated by dividing the sum of the two middle values by two. So in: 1, 2, 3, 4, 5, 6, the median is (3+4)/2, which equals 3.5.

The median is appropriate to use with ordinal variables, and with interval variables with a skewed distribution.

### Mode

The mode is the most common observation of a data set, or the value in the data set that occurs most frequently.

The mode has several disadvantages. It is possible for two modes to appear in the one data set (e.g. in: 1, 2, 2, 3, 4, 5, 5, both 2 and 5 are the modes).

The mode is an appropriate measure to use with categorical data.

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Updated: 15th August 2014 - 3:38pm
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