Social Research Glossary
Citation reference: Harvey, L., 2012-17, Social Research Glossary, Quality Research International, http://www.qualityresearchinternational.com/socialresearch/
This is a dynamic glossary and the author would welcome any e-mail suggestions for additions or amendments. Page updated 20 October, 2017 , © Lee Harvey 2012–2017.
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Averages are measures of central tendency and, as such, they provide a way to summarise data which gives an indication of the ‘centre’ of a set of data.
There are several different measures of average (measures of central tendency) including the arithmetic mean, the median, the mode, and the geometric mean.
Types of average
The arithmetic mean is sum of values of a variable for all the observations in a data set divided by the total number of observations.
This measure of central tendency corresponds to the common sense notion of ‘the average’.
It is only suitable for interval or ratio scales of data.
The geometric mean is in effect the mean of the product of the a set of values. It is computed by multiplying the n values together and then taking the nth root.
The measure is little used directly in the social sciences although it is integral to a number of sampling statistics as well as correlation coefficients and regression parameters. In most cases the geometric mean of just two terms is computed, which involves multiplying them together and taking the square root.
The median is the middle value of a set of values of a variable when ranked in order. The median value is such that (in theory) there as many items in the set above the median as below it. In practice, where the data is discrete and the median is computed to the nearest unit then there may not be exactly as many items below as above. However, in such circumstances the median will be the point at which the set of values is most nearly divided into two equal halves.
The mode is the most frequently occurring value of a set of observations. The mode is the simplest type of average and is the only one that can be used on nominal data.
The modal category is the category containing the greatest number of observations. When a distribution has several distinct values around which observations tend to cluster it is referred to as a multi-modal distribution; when it has two distinct values around which the observations cluster it is referred to as a bi-modal distribution.
Colorado State University (1993–2013) defines:
Central Tendency: These measures indicate the middle or center of a distribution.
Mode The most frequent score in a distribution.
Median The center score in a distribution.
Mean The average score within a distribution.
Elwell's Glossary of Sociology (undated) states:
MEAN. A statistical measure of 'central tendency' or average based on dividing a total by the number of individual cases involved. The mean is very sensitive to extreme scores. For example, the average life expectancy for people in a society with high infant mortality would be a misleading measure.
MEDIAN. The number that falls halfway in a range of numbers--the score below which are half the scores and above which are the other half. The median is a way of calculating 'central tendency' which is sometimes more useful than calculating a mean (particularly when many extreme scores are in the distribution).
MODE. The value that appears most often in a given set of data. This can sometimes be a helpful way of portraying central tendency.
Eurostat (2013) defines:
The geometric mean, sometimes also called geometric average, is an average calculated by multiplying a set of positive values and taking the nth root, where n is the number of values. The geometric mean is used to minimize the effects of extreme values; for instance, when averaging growth rates.
Colorado State University, 1993–2013, Glossary of Key Terms available at http://writing.colostate.edu/guides/guide.cfm?guideid=90 , accessed 12 December 2016.
accessed 12 December 2016.
Elwell's Glossary of Sociology, undated, available at http://campus.murraystate.edu/academic/faculty/frank.elwell/prob3/glossary/socgloss.htm, page not available 20 December 2016.
Eurostat , 2013, Glossary:Geometric mean, available at http://ec.europa.eu/eurostat/statistics-explained/index.php/Glossary:Geometric_average, last modified on 22 November 2013, accessed 3 January 2017.
copyright Lee Harvey 2012–2017
copyright Lee Harvey 2012–2017