1. T03-03 - 1 T03-02 Histogram (Empirical & Chebyshev) PurposeAllows the analyst to analyze quantitative data by summarizing it in sorted format, scattergram by observation, frequency dot plot by data value, and frequency histogram based on the standard deviation of the observed data. The template also compares the resulting relative frequency histogram to the expected normal relative frequency and Chebyshev's relative frequency based on the standard deviation of the observed data. Inputs Original Quantitative DataSorted Data Outputs Original Data Scattergram Sorted Quantitative Data Frequency Dot Plot Frequency Histogram Frequency versus Normal & Chebyshev Limitations 1000 quantitative data

2. T03-03 - 2 An Example A college professor has the test results shown here. He is interested in the producing a Histogram based on the Mean and Standard Deviation of the data. Also, he would like to compare the resulting histogram to the Empirical Rule and Chebyshev’s Theorem.

3. T03-03 - 3 Empirical Rule & Chebyshev’s Theorem Empirical Rule – mound shaped distributions The Interval Within Contains Approximately 1 Std Dev of the mean 68% of the data 2 Std Dev of the mean 95% of the data 3 Std Dev of the mean 99.7% of the data Chebyshev’s Theorem – non-mound shaped distributions The Interval Within Contains At Least 2 Std Dev of the mean 75% (3/4) of the data 3 Std Dev of the mean 89% (8/9) of the data

4. T03-03 - 4 Data can either be entered directly into the Original Data cells or copy/paste special/values into the cells.

5. T03-03 - 5 Once the data is entered the Mean, Standard Deviation, Count, Maximum, Minimum, and Standard Deviation Bins are automatically calculated.

6. T03-03 - 6 The Sort Macro can be run to sort the Original Data into the Sorted Data cells. This also automatically calculates the necessary information for the Dot Plot. The Histogram Macro calculates the Frequency by Bin.

7. T03-03 - 7

8. T03-03 - 8 The Scattergram displays a plot of the observations in the sequence they were entered.

9. T03-03 - 9 The Dot Plot displays a frequency plot of the observations.

10. T03-03 - 10 The Frequency Histogram for the Standard Deviation Bins is shown here.

11. T03-03 - 11 The Observed Histogram (relative frequency) is compared to the Empirical Rule and Chebyshev’s Theorem.