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Summary StatisticsWhen scientists are working with large amounts of data, or are trying to make some prediction about future trends, they use satatistics to summarize the information they have. Summary statistics are numerical representations of a data set. They are displayed through graphs, charts, tables, and raw calculations. It is important to understand the basics of statistics because data is often manipulated. If you understand statistics, then you can make education decisions about your data set based on the statistics you are given. For instance, look at the following three representations of the same data set. Notice how the observer's opinion can be altered by the way the data is presented. By the end of this module, you should be able to understand how to read each of these graphs and come to the same conclusions about the data set.
Central TendenciesThe most common summary statistics are the central tendencies. You can think of measures of central tendency as a way to identify the "middle" of a data set. Scientists use three methods to calculate central tendencies: mean, median and mode. Each of these will be discussed in detail in the following sections.MeanThe mean, also known as the arithmetic average, is the sum of all experimental data values divided by the total number of values. It is represented by an x (or other variable name) with a bar over it ( ) for a sample, and by the greek chracter mu (m) for a population.The mean for a sample is represented by:
Where: n = the number of data values in our set i ranges from 1 to n . (For example x2= the 2nd data value in our set.) In our practice data set below, n = 6 and x2 = 307. Try calculating the mean for this example. Do you get the same mean?
Nitrogen Dioxide (NO2) Concentrations 0.05 m Above the Surface
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