# visual presentations of data

The purpose of descriptive statistics is to describe the data, hence descriptive statistics is a communication science. There is a trade-off between presenting all the data, which is too much to comprehend, and presenting a portion of the data which does not contain all the information, but can be comprehended. The objective is to find the essence of the data which is important and present that, while ignoring aspects of the data which are distractions.

It is necessary to distinguish between categorical (qualitative, nominal, ordinal) data such as colors, flavors, type of gemstone which allows no manipulation of the categories versus quantitative (interval, ratio) data such as height and weight which are identified with the real numbers and can be manipulated as such. This course will be concerned with quantitative data.

A first approach to presenting quantitative data is to form a stem-and-leaf plot. One decides on a demarcation position, and the digits to the left of that position are the stems, while the digits to the right are the leafs. Listing all the leafs after a common stem, one produces what looks like a bar chart. The only information which has been lost is the order inwhich the data was collected. There are of course variations on preparing stem-and-leaf plots, such as subdividing stems into multiple stems, and truncating the data entries so that each has only one digit in a leaf.

Histograms group data like stem-and-leaf plots, but the categories are not constrained by the decimal structure of the numbers. Each category should be the same size, and the categories should be contiguous. Every datum must be in exactly one category or class. The actual values of the original data are not retained, but it is known how many data are in each class. Visually, a histogram looks like a bar chart.