As an example of the cumulative distribution, we will build and analyze the cumulative frequency distribution for rolling two standard number cubes.
Analysis:
If we sum all possible combinations from two standard cubes, we will get the following values:
| N/N | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Each value has its frequency and probability, see table below:
| Value | Frequency | Cumulative frequency | Probability |
|---|---|---|---|
| ⩽ 2 | 1 | 1 | 1/36 |
| ⩽ 3 | 2 | 2+1=3 | 2/36 |
| ⩽ 4 | 3 | 3+3=6 | 3/36 |
| ⩽ 5 | 4 | 6+4=10 | 4/36 |
| ⩽ 6 | 5 | 10+5=15 | 5/36 |
| ⩽ 7 | 6 | 15+6=21 | 6/36 |
| ⩽ 8 | 5 | 21+5=26 | 5/36 |
| ⩽ 9 | 4 | 26+4=30 | 4/36 |
| ⩽ 10 | 3 | 30+3=33 | 3/36 |
| ⩽ 11 | 2 | 33+2=35 | 2/36 |
| ⩽ 12 | 1 | 35+1=36 | 1/36 |
The cumulative frequency graph can be built according to the values in the table:
Position of the median:
The Median:
– from the graph, round to the nearest integer as for discrete structure
Position of the lower quartile:
Lower quartile:
– from the graph, round to the nearest integer as for discrete structure
Position of the upper quartile:
Upper quartile:
– from the graph, round to the nearest integer as for discrete structure
Interquartile range:
This tells us that the difference between maximal and minimal value in the middle 50% is equal 4.
References
Liu, Stanley T. Experimental And Analytical Investigation Of Solar Radiant Flux Distribution On Interior Surfaces Of A Sunspace. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards, 1986. Print.
Salkind, Neil J. Encyclopedia Of Research Design. Thousand Oaks, Calif.: Sage, 2010. Print.
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