# Cumulative Frequency Distribution Table Sample

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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