Summary Statistics

The simplest way to measure the key characteristics of a data set is to estimate the summary statistics for the data. For a data series, Xx, X2, X3, X„, 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

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)

The standard deviation is the square root of the variance. The mean and the standard deviation are the called the first two moments of any data distribution. A normal distribution can be entirely described by just these two moments; in other words, the mean and the standard deviation of a normal distribution suffice to completely characterize it. If a distribution is not symmetric, it is considered to be skewed and the skewness is the moment that describes both the direction and the magnitude of the skewness.

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