- the variance & standard deviation provide a measure of how dispersed the data values (x) are about the mean value (x^).
- because of its close links with the mean, the standard deviation can be greatly affected if the mean gives a poor measure of central tendency.
- the coefficiet of variation represents the ratio of the standard deviation to the mean, & it is a useful statistic for comparing the degree of variation from one data series to another.
- standard deviations vary according to the size of values in the distribution and may not even be in the same unit of measurement.
- for example, if the coefficient of variation is 10% then this mean that the standard deviation is equal to 10% of the average.
- for some measures, the standard deviation changes as the average changes.
- in this case, the coefficient of variation is the way to summarize the variation.
- a box plot is a way of summarizing a set data measured on an interval scale. It is often used in exploratory data analysis. It is a type of graph which is used to show the shape of the distribution, its central value & spread. The picture produced consists of the most extreme values in the data set [max & min ], the lower & upper quartiles & the median.
- box plots are very useful when large numbers of observations are involved & when two/more data sets are being compared. They are helpful for indicating whether distribution is skewed & whether there are any unusual observations [outliers] in the data set.
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