Pictures and data distributions

Frequency Tables

Frequency means how often something occurs. A frequency table puts data into a nice readable form of how often a piece of data occurs in the data set. It will also show the percentage. We have two types of percentages shown, relative frequency and cumulative frequency. The relative frequency simply states the % that the particular data point occurred whereas the cumulative frequency sums up each relative frequency as you go down the table until you reach 100%. This indicates you have accounted for all the data. Sometimes this number does not add up to exactly 100% because of rounding, but it should be very close!

The example below shows the frequency table of rolling a pair of dice 10 times

Frequency Table for Number Rolled on 2 dice
Number Rolled	Frequency	Relative Freq.	Relative Cumulative Freq.
2	1	1/10=.1=10%	10%
3	0	0%	10%
4	0	0%	10%
5	2	2/10=.2=20%	30%
6	1	1/10=.1=10%	40%
7	3	3/10=.3=30%	70%
8	3	3/10=.3=30%	100%

 

For any frequency table you do for this class please include relative and relative cumulative frequencies.

Sometimes we bin data when it is impossible to have a category for every value in the data set. The bins cover a range of data.

Frequency Table Height Of  20 Students at MCC
Height in inches	Frequency	Relative Freq.	Relative Cumulative Freq.
50-54	4	4/20=.2=20%	20%
55-59	8	8/20=.4-40%	60%
60-64	4	4/20=.2=20%	80%
65-69	0	0/20=0%	80%
70-74	4	4/20=.20=20%	100%
75-79	0	0%	100%

 

Notice the bins must be the same width and cannot overlap.

Picturing Distributions/Histograms

·  More on Histograms

A histogram is a plot that lets you discover, and show, the underlying frequency distribution (shape) of a set of continuous data. This allows the inspection of the data for its underlying distribution (e.g., normal distribution), outliers, skewness, etc. An example of a histogram, and the raw data it was constructed from, is shown below:

 

36	25	38	46	55	68	72	55	36	38
67	45	22	48	91	46	52	61	58	55