# AP Statistics Curriculum 2007 EDA Statistics

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Variables can be summarized using statistics.| Variables can be summarized using statistics.  
*A '''statistic''' is a numerical measure (or a function) that describes a characteristic of the ''sample''.| *A '''statistic''' is a numerical measure (or a function) that describes a characteristic of the ''sample''.  
-| *A '''parameter''' is a numerical measure that describes a characteristic of the ''population''.| +| *A '''parameter''' is a numerical measure that describes a characteristic of the ''population''. We use statistics to estimate parameters.  
-| We use statistics to estimate parameters.| +  
* We use '''sample-statistics''' to estimate/understand '''population parameters''' or characteristics!| * We use '''sample-statistics''' to estimate/understand '''population parameters''' or characteristics!  
+| * '''Notation''':   
+| ** Population parameters are typically denoted by lower-case Greek letters (e.g., <math>\mu, \sigma, \pi</math>, etc.)  
+| ** Random variables are always denoted by capital letters (e.g., ''X, Y, U, W'', etc.) and specific measurements (an instance of a data sample) are denoted by lower-case letters (e.g., ''x, y, u, w'', etc.).  
+| ** Data (sample) driven estimates (for specific population parameters) are always denoted by a corresponding symbol with an over-line or a hat (e.g., <math>\hat{\mu}, \overline{y}, \hat{\sigma}, \hat{p}</math>, etc.)  
===Example===| ===Example===  
-| Suppose we are interested in the ~~meancalory~~ or mean sodium content of hot dogs. It would be difficult to obtain measures of ~~calory~~ and salt content for ALL hot-dogs. However, we can use the [[SOCR_012708_ID_Data_HotDogs | Hot dogs ~~datafile~~]] that we discussed ~~uearlier~~. This data contains a sample of 54 major hot dog brands. Some of the interesting '''population ~~papameters~~ ''' are the mean-~~calory~~ , ~~mean~~ -sodium~~, variance~~ -~~of-calory between hot-dogs and~~ variance~~-of-sodium~~ between hot-dogs. These measures may be estimated from the sample using the corresponding '''sample-statistics''' (sample-averages and sample-variances). | +| Suppose we are interested in the mean calorie or mean sodium content of hot dogs. It would be difficult to obtain measures of calorie and salt content for ALL hot-dogs. However, we can use the [[SOCR_012708_ID_Data_HotDogs | Hot dogs data file]] that we discussed earlier. This data contains a sample of 54 major hot dog brands. Some of the interesting '''population parameters''' are the calorie-mean, sodium-mean, calorie-variance and sodium-variance between hot-dogs. These measures may be estimated from the sample using the corresponding '''sample-statistics''' (sample-averages and sample-variances).   
* Using [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and the [[SOCR_EduMaterials_ChartsActivities | Charts activities]] you can produce a number of interesting graphical summaries for [[SOCR_012708_ID_Data_HotDogs | this hotdogs dataset]].| * Using [http://socr.ucla.edu/htmls/SOCR_Charts.html SOCR Charts] and the [[SOCR_EduMaterials_ChartsActivities | Charts activities]] you can produce a number of interesting graphical summaries for [[SOCR_012708_ID_Data_HotDogs | this hotdogs dataset]].  
-| * The ~~histogram~~ of the '''~~Calory~~ ''' content of all hotdogs ~~in~~ shown in the image below. ~~Note~~ the ~~clear separation~~ of the ~~calories into 3 distinct sub-populations~~. ~~Could this be related to the type of meat in the hotdogs?~~|  +| * The '''dot-plot''' of the '''Calorie''' content of all hotdogs is shown in the image below. Notice the '''summary statistics''' of mean and standard deviation below the graph!  
+| <center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig7.jpg|500px]]</center>  
-| ~~< center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig3~~.~~jpg|500px]] </center>~~| +| * The '''dot-plot''' of the '''Sodium''' content of all hotdogs is shown in the image below. Notice the '''summary statistics''' of mean and standard deviation below the graph!  
-| ~~* The histogram of the '''Sodium''' content of all hotdogs in shown in the image below~~. ~~What patterns in this histogram can you identify? Try to explain!~~|  +| <center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig8.jpg|500px]]</center>  
-| ~~< center>~~[[~~Image:SOCR_EBook_Dinov_EDA_012708_Fig4.jpg~~ |~~500px~~]]~~< /center>~~| +| ===[[EBook_Problems_EDA_Statistics | Problems]]===  
<hr>| <hr>  
  
## Current revision as of 18:53, 28 June 2010

## Contents

  * 1 General Advance-Placement (AP) Statistics Curriculum - Statistics
    * 1.1 Definitions
    * 1.2 Example
    * 1.3 Problems
    * 1.4 References

  
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##  General Advance-Placement (AP) Statistics Curriculum \- Statistics

###  Definitions

Variables can be summarized using statistics. 

  * A **statistic** is a numerical measure (or a function) that describes a characteristic of the _sample_. 
  * A **parameter** is a numerical measure that describes a characteristic of the _population_. We use statistics to estimate parameters. 
  * We use **sample-statistics** to estimate/understand **population parameters** or characteristics! 
  * **Notation** : 
    * Population parameters are typically denoted by lower-case Greek letters (e.g., μ,σ,π, etc.) 
    * Random variables are always denoted by capital letters (e.g., _X, Y, U, W_ , etc.) and specific measurements (an instance of a data sample) are denoted by lower-case letters (e.g., _x, y, u, w_ , etc.). 
    * Data (sample) driven estimates (for specific population parameters) are always denoted by a corresponding symbol with an over-line or a hat (e.g., , etc.) 



###  Example

Suppose we are interested in the mean calorie or mean sodium content of hot dogs. It would be difficult to obtain measures of calorie and salt content for ALL hot-dogs. However, we can use the  Hot dogs data file that we discussed earlier. This data contains a sample of 54 major hot dog brands. Some of the interesting **population parameters** are the calorie-mean, sodium-mean, calorie-variance and sodium-variance between hot-dogs. These measures may be estimated from the sample using the corresponding **sample-statistics** (sample-averages and sample-variances). 

  * Using SOCR Charts and the  Charts activities you can produce a number of interesting graphical summaries for  this hotdogs dataset. 


  * The **dot-plot** of the **Calorie** content of all hotdogs is shown in the image below. Notice the **summary statistics** of mean and standard deviation below the graph! 



  * The **dot-plot** of the **Sodium** content of all hotdogs is shown in the image below. Notice the **summary statistics** of mean and standard deviation below the graph!