AP Statistics Curriculum 2007 EDA Freq

General Advance-Placement (AP) Statistics Curriculum - Summarizing data with Frequency Tables

Summarizing data with Frequency Tables & Histograms

There are two ways to describe a data set (sample from a population) - Pictorial Graphs or Tables of Numbers. Both are important for analyzing data.

Definitions

• A frequency distribution is a display of the number (frequency) of occurrences of each value in a data set.
• A relative frequency distribution is a display of the percentage (ratio or frequency to sample-size) of occurrences of each value in a data set.
• A percentile is the value of a variable that divides the real line into two segments - the left one containing certain percentage (say 13%) of the observations for the specific process, and the right interval containing the complementary percentage of observations (in this case 87%). The 30^th percentile is the value (measurement) bound above 30% and below 70% of the observations from a process.
• The (three) quartiles are the special cases of percentiles for Q₁=25%, Q₂=50% (median) and Q₃=75%.

Example

The table below shows the stage of disease at diagnosis of breast cancer in a random sample of 2092 US women.

Stage	Frequency	Relative Frequency
0	197	0.09
I	691	0.33
II	703	0.34
III	314	0.15
IV	187	0.09
Total	2092	1.00

Computational Resources: Internet-based SOCR Tools

• SOCR Charts allows you to generate graphical representations (including frequency histograms) of a variety of datasets.
• The SOCR Charts activities provide usage-instructions, examples and demonstrations of how to use SOCR Charts.

Hands-on activities

You can copy and paste the first 2 columns in the data table above in the SOCR Charts (BarChart --> XYPlot --> HistogramDemo7). You can see this SOCR Charts activity for help with histogram plots.

• The graph below illustrates the (raw) frequency histogram (using counts)

• The graph below shows the relative frequency histogram (using the last column of the table above).

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References

• Lecture notes on EDA

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• SOCR Home page: http://www.socr.umich.edu

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