Distribution - Measures of (center|central tendency) (Mean, Median, Mode)


A Measure of central tendency is a measure that describes the middle or center point of a distribution. A good measure of central tendency is representative of the distribution.

The mean, the median and the mode are measures of center.

Mean Vs Median

  • The mean is the most used measure as calculation of the central tendency.

The Mean (average) is the best measure of central tendency when the distribution is normal

  • Median (middle score) is preferred when there are extreme scores in the distribution

In a negatively skewed distribution, the median will be a little bit greater than the mean and in a positive skewed distribution, the median will be a little bit lower than the mean.

Example: Outliers Resistant

With the following Scores: 2 7 8:

  • the median is 7
  • and the Mean is 5,6

The better measure of your performance is the median.

The mean and median are so different because there is one score that is extremely different from the rest. In statistics, such extreme values are called outliers

The mean is affected by the presence of an outlier; however, the median is not.

A statistic that is not affected by outliers is called resistant.

The median is a resistant measure of center, and the mean is not resistant.

As a result, when we have a data set that contains an outliers, it is better to use the median to describe the center, rather than the mean.

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