How to Combine Data Points and Probability Densities

Stock market graphs provide common examples of data sets with probability curves.

Determining the relationship between an existing data point set and a probability density occurs best when visualizing the two on the same graph. From a statistics perspective the exercise involves basic plotting and graphing and then estimating the likelihood of repeat results based on existing patterns. When data clumps visually on such a graph, it indicates higher probability of that result than other possibilities, a probability density curve can be concluded and used as a prediction tool.

Things You'll Need

• Graphing paper
• Pencil
• Graphing calculator
• Red pencil

Instructions

1. Collect your data points as they exist for a set a time range by recording observations of targeted behavior and measurement. Plot out the data on a paper graph field. Create the graph using appropriate variables as the vertical and horizontal axis lines for the graph. For example, a data set with results over time would have the results measured as a metric on the Y axis vertically and the time period measured on the X axis horizontally.

2. Draw pencil marks for the data points on the graph as they correspond with your axis values. Use a third or fourth axis for multi-variable data sets to produce three-dimensional data graphs.

3. Look at the existing data points displayed graphically. Use a red pencil to circle areas on the graph where a predominant amount of data points "clump" or group together visually.

4. Write an algebra or calculus formula into a graphing calculator that when calculated visually represents a constant performance line connecting the groups of data to each other. Draw this formula on the paper graph by providing a calculated value for each variable in the math formula, changing it sequentially until the probability curve becomes apparent visually.

5. Draw the math formula graphic result on to the graph of the data point set to see the combined result. Reproduce the combined dual-graph image on a clean sheet of paper to visualize the actual data points with the probability curve.

Tips & Warnings

• Computer software exists that can be used both data point input and graphic mapping of the information. Using these kinds of software tools can make statistical graphing far easier than on paper.

• Double-check your math formula to be sure that it operates consistent with your actual data. Inputting the incorrect value for adjustments can cause your probability curve to veer wildly off course versus your actual data behavior.

References

• College of Saint Benedict & Saint John's University: Display of Statistical Distribution
• Quick-R; Probability Plots; Robert Kabicoff; 2011
• Mathwave: Probability Density Function (PDF) Graph
• MathWorks: Distribution Plots: 2011