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Analysis of Data: Common Descriptive and Summary Statistics

Summary statistics are a good place to start the analysis; however, be careful not to interpret data using only summary statistics. In addition, it is important to check the distribution of the data – most environmental data are not normally distributed.
Arithmetic mean – sum of the observations (data) divided by the number of observations.
Median – the midpoint of a distribution (observations in order from smallest to largest).

Distributions (is the data normally distributed?)
Geometric mean – often useful summaries for skewed data, such as bacteria (E. coli).

Measures of variability (standard deviation, coefficient of variability, skewness.)
Box and whisker plots (five number summary) describe the center and the spread of the data.
Mean and median – assess the center of a distribution.
They are the same if the distribution is symmetric (Figure 5); in a skewed distribution, the mean is pulled towards a tail (Figure 6).

It is important to be able to identify outliers in data and understand the implications of and data analysis with and without outliers.