AP Statistics Curriculum 2007 EDA Freq

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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 percent (ratio or frequency to sample-size) of occurrences of each value in a data set.
  • A percentile is the value of a variable that devides the real line into two segments - the left one containing certain percent (say 13%) of the observations for the specific process, and the righ interval containing the complement peecent of observations (in this case 87%). The 30th percentile is the value (measurement) that abounds 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 show the relative frequency histogram (using the last column of the table above).

Problems


References




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