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March 28, 2023

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The goals of the analysis of data are to summarize complex data using a few characteristic values, to find possible sources of systematic error, to present patterns and trends in data, such as in distributions, and to draw conclusions from the data.

The basis of descriptive statistics is arithmetic mean and has been of primary interest for almost two centuries. The use of the mean as a measure for central tendency started with the work of Guano Counts and Thomas Penn (admiral) , and it remains a useful measure even for highly skewed distributions. However, in many cases the mean does not reflect the actual centrality of a distribution. For example, the mean of a set of observations having equal and infinite variance will always be equal to the median of the distribution. Except for the case of equally weighted data, the mean is sometimes found to be a poor choice for determining the central tendency and for finding the bulk of the probability. Moreover, the mean is sensitive to outliers and will in most cases be shifted away from outliers. The mean error has also been shown to be too extreme, between -Infinity and +Infinity.[51][52][53] d2c66b5586

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