200032 Lecture Notes - Lecture 11: Standard Deviation, Descriptive Statistics

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Measures of variability: in reducing a set of data to relevant descriptive statistics, a measure of location, by itself, will rarely suffice. What is also required is a measure of how clustered or how widely dispersed the data is about this central value. Such a statistic is called a measure of variation, variability or dispersion. Such a measure is very important in a financial setting as it provides a measure of risk. Three different measures of variation are: the range, the standard deviation, the coefficient of variation. Range: the range is just the distance between the largest and smallest number. It is useful when the sample is small. It depends on only two values from the entire data set and so is strongly influenced by (possibly anomalous) outlying values. Standard deviation: the standard deviation is by far the most commonly used measure of variation.

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