800:173 Probability and Statistics

Additional Definitions

Arithmetic mean

This is what is usually called the mean, add up the data values and divide by n.

Geometric mean

This is the nth root of the product of the data values; it can be obtained by exponentiating the arithmetic mean of the logarithms of the data values. It is useful for finding average rates of growth (e.g., interest).

Harmonic mean

This is the reciprocal of the arithmetic mean of the reciprocals of the data. One use is finding the average speed when driving specified distances at specified speeds.

Maximum, minimum

These can be interpreted as averages. They are useful when deciding whether a convoy of vehicles can drive over a bridge, or you can take all your nephews on the roller coaster.

Mean deviation

This is the average absolute value of the distance of the data from the mean. Although this is usually defined as distance from the mean, it merits mention that the median is the value from which the mean deviation is least (the mean is the value from which the squared deviation is least).

Coefficient of variation

The coefficient of variation is the quotient of the standard deviation by the mean. It is useful if one wants to compare the amount of variation in the weight of mice with the variation in men.

Quartiles

There are several definitions used to calculate quartiles, which will result in different values, especially for small data sets. But this entry is included to stress that present usage defines quartiles as values (cutoffs), not ranges. There is no fourth quartile, a person in the top fourth of the class is above the third quartile, not in the fourth quartile. Data is above, below, or at a quartile, not in a quartile.

Ogive

An ogive is a cumulative distribution version of a histogram. It is named for an architectural feature of many cathedrals which suchcurves often resemble.

August 1999
campbell@math.uni.edu
http://www.math.uni.edu/~campbell