# AP Statistics Curriculum 2007 EDA Freq

(Difference between revisions)
 Revision as of 19:40, 27 January 2008 (view source)IvoDinov (Talk | contribs) (→Hands-on activities)← Older edit Current revision as of 18:44, 28 June 2010 (view source)Jenny (Talk | contribs) (→Definitions) (8 intermediate revisions not shown) Line 6: Line 6: ===Definitions=== ===Definitions=== * A '''frequency distribution''' is a display of the number (frequency) of occurrences of each value in a data set. * 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 '''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 [http://en.wikipedia.org/wiki/Percentile 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 30th 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=== ===Example=== - Stage of disease at diagnosis of breast cancer in a random sample of US women. + The table below shows the stage of disease at diagnosis of breast cancer in a random sample of 2092 US women. +
{| class="wikitable" {| class="wikitable" |- |- Line 41: Line 44: | 1.00 | 1.00 |} |} +
===Computational Resources: Internet-based SOCR Tools=== ===Computational Resources: Internet-based SOCR Tools=== Line 47: Line 51: ===Hands-on activities=== ===Hands-on activities=== - You can copy the first 2 columns in the data table above ans paste it in the [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] (BarChart --> XYPlot --> HistogramDemo7). You can see [[SOCR_EduMaterials_Activities_Histogram_Graphs | this SOCR Charts activity]] for help with histogram plots. + You can copy and paste the first 2 columns in the data table above in the [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] (BarChart --> XYPlot --> HistogramDemo7). You can see [[SOCR_EduMaterials_Activities_Histogram_Graphs | this SOCR Charts activity]] for help with histogram plots. * The graph below illustrates the (raw) frequency histogram (using counts) * The graph below illustrates the (raw) frequency histogram (using counts)
[[Image:SOCR_EBook_Dinov_EDA_012708_Fig1.jpg|500px]]
[[Image:SOCR_EBook_Dinov_EDA_012708_Fig1.jpg|500px]]
- * The graph below show the relative frequency histogram (using the last column of the table above). + * The graph below shows the relative frequency histogram (using the last column of the table above).
[[Image:SOCR_EBook_Dinov_EDA_012708_Fig2.jpg|500px]]
[[Image:SOCR_EBook_Dinov_EDA_012708_Fig2.jpg|500px]]
+ + ===[[EBook_Problems_EDA_Freq | Problems]]===

## 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 30th 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).