Central Measures

Measures of central tendencies are nothing but the measures to describe the "central" values of a collected sample. For an ungrouped set of data these measures are: the mean, the median, and the mode.

The arithmetic mean, or the simple mean, is computed by summing all numbers in an array of numbers (x_i) and then dividing by the number of observations (N) in the array.

; the sum is over all i's.

The mean uses all of the observations, and each observation affects the mean. Even though the mean is sensitive to extreme values - that is extremely large or small data can cause the mean to be pulled toward the extreme data - it is still the most widely used measure of location.

This is due to the fact that the mean has valuable mathematical properties that make it convenient for use with inferential statistical analysis.

For example:

• the sum of the deviations of the numbers in a set of data from the mean is zero; and

• the sum of the squared deviations of the numbers in a set of data from the mean is the minimum value.

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Next: The Median