Central Tendency Measure

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A Central Tendency Measure is a measurement of the central value for a probability distribution.



References

2015

The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value." [2][3]
The central tendency of a distribution is typically contrasted with its dispersion or variability ; dispersion and central tendency are the often characterized properties of distributions. Analysts may judge whether data has a strong or a weak central tendency based on its dispersion.


Mean
The most common way of measuring the center point of a set of measurements is with the average, or mean (i.e. the sum of all measurements divided by the total number of measurements).
The mean is useful for further mathematical treatment, as it considers all values (although a few extreme values can cause the mean to become unrepresentative of the rest of the values).
Median
If the measurements are listed in numeric order, then the median is the number half-way down the list. If there is an even number of measurements, it is half-way between the middle two numbers. The median is not distorted by extreme values, but it can be very unrepresentative of the other values, particularly in a distribution which is not symmetrical.
Mode
The mode is the most commonly occurring measurement. In a distribution graph, this is the highest point. The mode is also not distorted by extreme values, and is useful for measuring such as average earnings. However, there can be more than one mode, and it is not as good as the mean for mathematical treatment.
In a symmetrical distribution such as a Normal distribution, these three measures are the same. In an asymmetrical (or skewed) distribution, as below, there is a simple rule-of-thumb formula which can be used to estimate one, given the other two: Mean - Mode = 3 x (Mean - Median)


  1. Weisberg H.F (1992) Central Tendency and Variability, Sage University Paper Series on Quantitative Applications in the Social Sciences, ISBN 0-8039-4007-6 p.2
  2. 2.0 2.1 Upton, G.; Cook, I. (2008) Oxford Dictionary of Statistics, OUP ISBN 978-0-19-954145-4 (entry for "central tendency")
  3. Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP for International Statistical Institute. ISBN 0-19-920613-9 (entry for "central tendency")