Your software routinely gives you four descriptive statistics for your data: the average, the standard deviation, the skewness, and the kurtosis. Of these only the average is easy to understand. This article and the next illustrate what these statistics are telling you about your data.

Welcome to Statistics Summer Camp where we use building blocks to create digital distributions. With these distributions we can discover what the various statistics do, and do not, tell us about our data.

The average

When we compute an average we are creating a first-order simplification of the data. We are reducing them down to one characteristic. The average is that single value where we could place all of the data without changing the location of the data set as a whole. Thus, the average may be thought of as the balance point for the data. Of course, the data are not all equal to the average, and we do not usually draw a graph with all the data at the average, but for the purposes of describing our data, the average provides a first-order simplification of the data.

Our first example will consist of 24 values with an average of 9.000.

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