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AP Statistics Unit I: Describing patterns and departures from patterns Week 6 MM4A1. Students will explore rational functions. b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition. c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

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Exploring & Understanding Data Weeks 2 - 4 Describing patterns and departures from patterns (20%–30%) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries. Yates Chapters 1 - 4

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Exploring Data Week 2 A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. ShapeYates Chapter 1 B. Summarizing distributions of univariate data 1. Measuring center: median, mean 2. Measuring spread: range, interquartile range, standard deviation 3. Measuring position: quartiles, percentiles, standardized scores (z-scores) 4. Using boxplots 5. The effect of changing units on summary measures Yates Chapter 1

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Describing Location in a Distribution Weeks 3 - 4 C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) 1. Comparing center and spread: within group, between group variation 2. Comparing clusters and gaps 3. Comparing outliers and other unusual features 4. Comparing shapes D. Exploring bivariate data 1. Analyzing patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers and influential points 5. Transformations to achieve linearity: logarithmic and power transformations Yates Chapter 3 E. Exploring categorical data 1. Frequency tables and bar charts 2. Marginal and joint frequencies for two-way tables 3. Conditional relative frequencies and association 4. Comparing distributions using bar charts Test #1 at the end of this week

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Exploring & Understanding Data Week 2 Overview Monday 1.1 Displaying Data with Graphs Tuesday1.2 Describing Distributions with Numbers Wednesday 2.1 Measures of Relative Standing & Density Curves Thursday2.2 Normal Distributions Friday Quiz on Chapters 1 & 2 Describing patterns and departures from patterns (20%–30%) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

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Monday Essential Question: How are Distributions Displayed with Graphs? Opening/Middle Warm Up: Homework Review Middle Whole Class Reading p. 37 Silent Reading p. 38 -46 1.1 How to Read Math Text Graphic organizer notes on displaying data Tech Toolbox p. 59 Practice problems p. 46 # 3, 6, p. 55 #7,10 p. 64 #13, 16, 18 Middle/End I. Flow Chart for Displaying Data Comparison Chart of Histograms & Bar Graphs II. Examining Distributions III. Relative Frequency & Cumulative Frequency IV.Time Plots End Activity 1A p. 38 Tonights Homework p. 46 #1, p. 55 #8 p. 64 #14 p. 68 #25 Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Monday Essential Question: How are Distributions Displayed with Graphs? Warm Up: p. 106 #1.59 Opening Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Monday Essential Question: How are Distributions Displayed with Graphs? Categorical Displays Pie Charts Bar Graphs Quantitative Displays Stemplots Histograms Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Monday Essential Question: How are Distributions Displayed with Graphs? Do the data tell you what you want to know? Displaying Data Pie ChartsBar Graphs Stemplots (Stem & Leaf Plots) Histograms 1. 2. 3. 1. 2. 3. 4. 1. 2. 3. 4. Describing patterns and departures from patterns (20%–30%) Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.

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Monday Essential Question: How are Distributions Displayed with Graphs? Bar Graphs Use ______ the distribution of a _______ variable on the _________ axis. Detail Drawn with _____ between bars. Histograms Use _____ the distribution of _____ or ____ among the values of a single ________ variable. Detail Drawn with ___ spaces between bars. Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries. Technology Toolbox p. 59 Making Calculator Histograms

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Monday Essential Question: How are Distributions Displayed with Graphs? Patterns Shape Center Spread Deviations from Patterns ( ) Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries. Practice: Summer Activity Binder pp. 8 - 10 When examining distributions we are looking for two main things: Patterns & Deviations from Patterns Read p. 53 Example 1.7

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Tuesday Essential Question: How are Distributions Displayed with Graphs? Warm Up: p. 59 Technology Toolbox (10 min) Homework Review p. 46 #1, p. 55 #8 p. 64 #14, p. 68 #25 (10 min) Lecture/ Reading pp 69 – 74 (15 min) Discussion Problems #27, 40 Describing Distributions w/ Numbers Stations Tech Toolbox p. 81 Practice Problems #31, 43, 69 Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53 Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1 p. 55 #8 p. 64 #14 p. 68 #25

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1* p. 55 #8 p. 64 #14 p. 68 #25

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1 p. 55 #8 p. 64 #14 p. 68 #25 #8 a)The distribution is skewed right, with a median of 2. The mean of this distribution would be higher because of the skewness so the mean would be about 4 or 5. There are no apparent outliers. b) 15/65 =.23 = 23% of the time the temp never fell below freezing in April

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1 p. 55 #8 p. 64 #14 p. 68 #25 For additional example(s) of Split-Stem Leaf Plots visit http://www.statcan.gc.ca/ed u/power- pouvoir/ch8/5214816- eng.htm#a8 Rounding the values would yield: 140 160 110 150 130 100 100 80 170 200 270 100 170 360 150 150 Note: Now all of the ones digits are zeros. The split stem-leaf plot would look like: 0 (0) 0 (5) 8 1 (0) 000134 1 (5) 555677 2 (0) 0 2 (5) 7 3 (0) 3 (5) 6

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1 p. 55 #8 p. 64 #14 p. 68 #25

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 46 #1 p. 55 #8 p. 64 #14 p. 68 #25*

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Tuesday Essential Question: How are Distributions Described Using Numbers? Lecture/ Reading pp 69 – 74 (15 min) Discussion Problems #27, 40 Mean vs Median Tech Toolbox p. 81 Practice Problems #31, 43, 69 Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53 Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Tuesday Essential Question: How are Distributions Described Using Numbers? Measuring Spread A.Quartiles B.The Five-Number Summary & Box Plots C.The 1.5 X IQR Rule for Suspected Outliers

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Tuesday Essential Question: How are Distributions Described Using Numbers? Measuring Spread D.The Standard Deviation E.Choosing Measures of Center & Spread F.Changing the Unit of Measurement G.Comparing Distributions

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Tuesday Essential Question: How are Distributions Displayed with Graphs? Lecture/ Reading pp 69 – 74 (15 min) Discussion Problems #27, 40 Describing Distributions w/ Numbers Stations Tech Toolbox p. 81 Practice Problems #31, 43, 69 Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53 Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries.

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Homework Review p. 74 #27 p. 89 #41 p.97 #49 p. 100 #53

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Warm Up: Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Displaying Distributions A.Make an effective Stemplot B.Make a histogram C.Make an ogive of a set of quantitative data Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries

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Wednesday Essential Question: How are Distributions Displayed with Graphs? What is an ogive? Data may be expressed using a single line. An ogive (a cumulative line graph) is best used when you want to display the total at any given time. Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Make an ogive of a set of quantitative data Practice Problem p. 64 #1.14b

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Wednesday Essential Question: How are Distributions Displayed with Graphs? 0 0 1 4 4 4 6 7 7 7 10 15 What is a boxplot? 527

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Wednesday Essential Question: How are Distributions Displayed with Graphs? Why Use Boxplots? Boxplots help us to compare distributions side by side They also allow us to see the shape of the distribution Five Number Summary & Boxplots Minimum 1 st Quartile Median 3 rd Quartile Maximum min Q 1 Q 2 Q 3 max The Interquartile Range IQR Q 3 – Q 1 An observation may be an outlier if it falls more than 1.5xIQR above Q 3 or below Q 1 Technology Toolbox p. 81

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Wednesday Essential Question: How are Distributions Displayed with Graphs?

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Displaying Distributions A.Make an effective Stemplot B.Make a histogram C.Make an ogive of a set of quantitative data Pop Quiz Time!!! http://www.cliffsnotes.com/study_guide/Quiz-Introduction-to-Graphic- Displays.topicArticleId-267532,articleId-267448.html Standard: Describing patterns and departures from patterns Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis placed on interpreting information from graphical and numerical displays and summaries

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Warm Up: Thursday Essential Question: How are Distributions Displayed with Graphs? Tonights Homework: p. 97 #1.47 p. 102 #58 p. 110 #68 p. 111 #70

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Thursday Essential Question: How are Distributions Displayed with Graphs? Assessing Shape A.Look for overall patterns & for major deviations from patterns B.Determine whether or not the distribution is roughly symmetric, distinctly skewed, or neither. Look for modes C.Describe the overall pattern by giving numerical measures of center, spread and a verbal description of shape. http://stattrek.com/AP-Statistics-1/Data-isplay.aspx?Tutorial=AP

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Thursday Essential Question: How are Distributions Described Using Numbers? Mean Median 1.Found by ______________________ and dividing by the number of Observations 2.Known as the _________ value 3.Sensitive to the influence of _______________ 4.Can be found using the _________ 5.Takes into consideration the Value of each _______________ 1.Found by ____________ the observations and choosing the __________ value 2.The _____ percentile 3.Resistant to _________ values 4.Must be done by _______ or by _______________ 5.Only takes into consideration the ___________ of observations

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Thursday Essential Question: How are Distributions Displayed with Graphs? Inspecting Distributions (Quantitative Variables) D. Decide which measures of center & spread are more appropriate: For Symmetric Distributions & No Outliers the mean & standard deviation For Skewed Distributions or Strong Outliers the five-number summary E. Recognize Outliers IQR x 1.5

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Thursday Essential Question: How are Distributions Described Using Numbers? The Effects of Mean & Median on the Shape of Distributions 1. __________ If the mean = mode or they are very close to each other 2._________ If the mean is further out in the tail than the median

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Thursday Essential Question: How are Distributions Described Using Numbers? Comparing Distributions There are many ways to compare distributions: Side by side boxplots Side by side bar graphs Back to back stem-plots Are just a few. Read page 94 - 96 starting with Example 1.19 Do you feel comfortable deciding which comparison to use?

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Data Analysis Summary p. 93 Data: Organize & examine Data Graphs: Construct the appropriate graphical displays Numerical Summaries: Calculate relevant summary statistics Interpretation: Discuss what the data, graphs & numerical summaries tell you in the context of the problem. Answer the Question!

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Wrap Up Congratulations! You have just been hired as marketing director of one of the most prestigious firms in the region. Your first assignment is to convince your biggest client where and how to spend money on t.v. advertising. You and your team must complete the assignment on p. 102 Case Closed then write a convincing argument on why you choose that network. Remember to refer to p. 37 for the original data. Client List: Nike Walmart Exxon Mobil Ford Publix UGA Bank of America Toys R Us

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Friday Essential Question: How well do I understand how to explore data? Opening Warm Up: Homework Review

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Friday Essential Question: How well do I understand how to explore data? Middle Group Assignments & Presentations Quiz on Chapter 1 End Homework Read 2.1 page 116 – 152 Outline the section

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UNIT ONE REVIEW Exploring Data.

UNIT ONE REVIEW Exploring Data.

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