A Primer on Statistics

A Primer on Statistics

            Large amounts of data are often compressed into more easily assimilated summaries, which provide the user with a sense of the content, without overwhelming him or her with too many numbers. There a number of ways in which data can be presented. One approach breaks the numbers down into individual values (or ranges of values) and provides probabilities for each range. This is called a "distribution". Another approach is to estimate "summary statistics" for the data. For a data series, X1, X2, X3, ....Xn, where n is the number of observations in the series, the most widely used summary statistics are as follows –

•     the mean (, which is the average of all of the observations in the data series

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•     the median, which is the mid-point of the series; half the data in the series is higher than the median and half is lower

•     the variance, which is a measure of the spread in the distribution around the mean, and is calculated by first summing up the squared deviations from the mean, and then dividing by either the number of observations (if the data represents the entire population) or by this number, reduced by one (if the data represents a sample)

            When there are two series of data, there are a number of statistical measures that can be used to capture how the two series move together over time. The two most widely used are the correlation and the covariance. For two data series, X (X1, X2,.) and Y(Y,Y...  ), the covariance provides a non-standardized measure of the degree to which they move together, and is estimated by taking the product of the deviations from the mean for each variable in each period.

The sign on the covariance indicates the type of relationship that the two variables have. A positive sign indicates that they move together and a negative that they move in opposite directions. While the covariance increases with the strength of the relationship, it is still relatively...