Wednesday, September 5, 2012

The 3 measures of central tendency in a set of data is mean, median and mode.  The mean is the average of the set of numbers.  The median is the number in the middle of the set of data and the mode is the number that occurs most frequently. But how do we know which measure of central tendency is the best to use?

Take this example.

The data set is  2, 5, 6, 10, 12, 12, 13, 16, 20, 21, 23, 110

Mean is (2 + 5 + 6 + 10 + 12 + .... + 110)/12 = 20.8

Median is 12.5 (middle values are 12 and 13)

Mode is 12

Notice that the mean is much larger than the median and mode.  If you compare the average of 20.8 to the numbers in the set, only 3 numbers are higher.  The mean is not a good measure of central tendency in this case because of 110. Any outliers will greatly affect the mean.

 Generally, we use the median when the data set has an outlier, as in example above.

The mode is actually not really a measure of central tendency. It should only be used with nonnumeric data to state what item in the data set is most popular.

The distribution of the data also has some effect but I gave a simple example that will explain which to use, in general.

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