AP Statistics Curriculum 2007 EDA Statistics

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(New page: == General Advance-Placement (AP) Statistics Curriculum - Statistics== ===Definitions=== Variables can be summarized using statistics. *A '''statistic''...)
(Definitions)
 
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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''.
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*A '''parameter''' is a numerical measure that describes a characteristic of the ''population''.
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*A '''parameter''' is a numerical measure that describes a characteristic of the ''population''. We use statistics to estimate parameters.
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We use statistics to estimate parameters.
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* 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===
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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]].
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* 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?
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* 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!
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig7.jpg|500px]]</center>
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig3.jpg|500px]]</center>
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* 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!
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* 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!
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig8.jpg|500px]]</center>
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<center>[[Image:SOCR_EBook_Dinov_EDA_012708_Fig4.jpg|500px]]</center>
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===[[EBook_Problems_EDA_Statistics | Problems]]===
<hr>
<hr>

Current revision as of 18:53, 28 June 2010

Contents

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., \hat{\mu}, \overline{y}, \hat{\sigma}, \hat{p}, 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).

  • 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!

Problems


References




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