# AP Statistics Curriculum 2007 EDA Freq

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===Summarizing data with Frequency Tables & Histograms=== | ===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 [http://en.wikipedia.org/wiki/Percentile percentile] is the <u>value</u> 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<sup>th</sup> 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 Q<sub>1</sub>=25%, Q<sub>2</sub>=50% (median) and Q<sub>3</sub>=75%. | ||

- | + | ===Example=== | |

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

- | = | + | <center> |

- | + | {| class="wikitable" | |

- | + | |- | |

- | + | ! 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 | ||

+ | |} | ||

+ | </center> | ||

===Computational Resources: Internet-based SOCR Tools=== | ===Computational Resources: Internet-based SOCR Tools=== | ||

- | * | + | * [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] allows you to generate graphical representations (including frequency histograms) of a variety of datasets. |

+ | * The [[SOCR_EduMaterials_ChartsActivities | SOCR Charts activities]] provide usage-instructions, examples and demonstrations of how to use SOCR Charts. | ||

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- | |||

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- | |||

- | |||

===Hands-on activities=== | ===Hands-on activities=== | ||

- | + | 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) | ||

+ | <center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig1.jpg|500px]]</center> | ||

- | * | + | * The graph below shows the relative frequency histogram (using the last column of the table above). |

+ | |||

+ | <center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig2.jpg|500px]]</center> | ||

+ | |||

+ | ===[[EBook_Problems_EDA_Freq | Problems]]=== | ||

<hr> | <hr> | ||

+ | |||

===References=== | ===References=== | ||

- | * | + | * [http://www.stat.ucla.edu/%7Edinov/courses_students.dir/07/Fall/STAT13.1.dir/STAT13_notes.dir/lecture02.pdf Lecture notes on EDA] |

<hr> | <hr> |

## Current revision as of 18:42, 28 June 2010

## Contents |

## 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 Q_{1}=25%, Q_{2}=50% (median) and Q_{3}=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).

### Problems

### References

- SOCR Home page: http://www.socr.ucla.edu

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