Measures of Central Tendency

Measures of Central Tendency

These are a way of summarising large data sets into one single value, which summarises the data set. They are not specific statistical tests but achieve a similar objective, allowing easy comparison between data sets.

·         Mean

To get the mean of a data set you must add up all the results and divide by the number of results that you have.

This result is the average result of the data set, which all other results vary around; it is represented by the X-bar symbol shown above.

This is a useful measurement as it is quick and easy to calculate, and the result is usually a simple figure. The means of two data sets can be easily compared, showing if the results from the two sets are of similar value or widely different. It takes all the data into consideration, and the results is applicable for further mathematical processing to provide more information about the data set.

Although the mean is very useful, and one of the most widely used statistics it is easily distorted by extreme values; this makes data less reliable and is often used by companies to bias data, as one large value can make the mean appear to be much larger than it actually should be.

·         Median

This is the middle number of a data set, it is worked out by ranking the data in order; for small data sets the middle number will be obvious but for larger data sets the formula N+1 / 2 can be applied. N= the number of results in the data set, then you add 1 to this number, dividing by two then gives the position of the middle number not the value itself, find this position in the ranked data and that is the median. If there is an even number of results in the data set there will appear to be two median values, to overcome this the average of the two results must be calculated.

The median is a useful figure to compare to central value to two data sets to see if they are similar or widely different. The value is applicable for further mathematical processing to see if similarities or differences are statistically significant. The median value is also more accurate than the mean as it is not affected by extreme values; it shows nothing of the spread of data and only one figue from the data set.

• Mode

The mode is simply the value that occurs the most in a data set (Mode= Most Often). It is therefore very quick and easy to calculate, and remains unaffected by extreme values. Any data set with two modes is said to be bi-modal, with three it is tri-model etc, but comparing data sets with over three or four modal values would not be very useful.

The mode is not suitable for further mathematical processing and has limited value with numerical data sets. However it is very useful for analysing categories and questionnaire results, from which tally charts have been constructed; it would therefore be more applicable to human based geographical studies.

The measures of central tendency are all useful in their own right, in different ways for different data sets. The mode is a measure unique to certain types of data, and the median and mean are most informative when used together. These values are also made more useful through further statistical tests.