AP Statistics Unit I: Describing patterns and departures from patterns Week 6 MM4A1. Students will explore rational functions. b. Find inverses of rational.

AP StatisticsUnit I: Describing patterns and

departures from patterns

Week 6MM4A1. 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.

Exploring & Understanding DataWeeks 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

Exploring DataWeek 2

A. Constructing and interpreting graphical displays of distributions ofunivariate data (dotplot, stemplot, histogram, cumulative frequency plot)1. Center and spread2. Clusters and gaps3. Outliers and other unusual features4. Shape Yates Chapter 1

B. Summarizing distributions of univariate data1. Measuring center: median, mean2. Measuring spread: range, interquartile range, standard deviation3. Measuring position: quartiles, percentiles, standardized scores (z-scores)4. Using boxplots5. The effect of changing units on summary measures Yates Chapter 1

Describing Location in a DistributionWeeks 3 - 4

C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)1. Comparing center and spread: within group, between group variation2. Comparing clusters and gaps3. Comparing outliers and other unusual features4. Comparing shapes

D. Exploring bivariate data1. Analyzing patterns in scatterplots2. Correlation and linearity3. Least-squares regression line4. Residual plots, outliers and influential points5. Transformations to achieve linearity: logarithmic and power transformations Yates Chapter 3

E. Exploring categorical data1. Frequency tables and bar charts2. Marginal and joint frequencies for two-way tables3. Conditional relative frequencies and association4. Comparing distributions using bar charts

Test #1 at the end of this week

Exploring & Understanding DataWeek 2 Overview

Monday 1.1 Displaying Data with GraphsTuesday 1.2 Describing Distributions with NumbersWednesday 2.1 Measures of Relative Standing & Density CurvesThursday 2.2 Normal DistributionsFriday 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.

Monday

Essential Question: How are Distributions Displayed with Graphs?

Opening/MiddleWarm Up:Homework Review

MiddleWhole Class Reading p. 37Silent Reading p. 38 -461.1 How to Read Math Text Graphic organizer notes on displaying dataTech Toolbox p. 59 Practice problemsp. 46 # 3, 6, p. 55 #7,10 p. 64 #13, 16, 18

Middle/EndI. Flow Chart for Displaying DataComparison Chart of Histograms & Bar Graphs II. Examining DistributionsIII. Relative Frequency & Cumulative FrequencyIV.Time PlotsEndActivity 1A p. 38Tonight’s Homework p. 46 #1, p. 55 #8 p. 64 #14 p. 68 #25

Standard: Describing patterns and departures from patternsExploratory 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.

Monday


Warm Up: p. 106 #1.59

Opening


Monday


Categorical DisplaysPie Charts

Bar Graphs

Quantitative DisplaysStemplots

Histograms


MondayEssential Question:

How are Distributions Displayed with Graphs?

Do the data tell you what you want to know?

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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.



Bar GraphsUse ______ the distribution of a _______ variable on the _________ axis.

DetailDrawn with _____ between bars.

HistogramsUse_____ the distribution of _____ or ____ among the values of a single ________ variable.DetailDrawn with ___ spaces between bars.


Technology Toolbox p. 59 Making Calculator Histograms



Patterns Shape

Center

Spread

Deviations from Patterns

( )


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

Tuesday


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, 40Describing Distributions w/ Numbers StationsTech Toolbox p. 81

Practice Problems #31, 43, 69

Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53


Wednesday


Homework Reviewp. 46 #1p. 55 #8 p. 64 #14p. 68 #25

Wednesday


Homework Reviewp. 46 #1*p. 55 #8 p. 64 #14p. 68 #25

Wednesday



#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

Wednesday



For additional example(s) of Split-Stem Leaf Plots visithttp://www.statcan.gc.ca/edu/power-pouvoir/ch8/5214816-eng.htm#a8

Rounding the values would yield:140 160 110 150 130 100 100 80170 200 270 100 170 360 150 150Note: Now all of the one’s digits are zeros.

The split stem-leaf plot would look like:0(0)

0 (5) 81(0) 000134 1(5) 5556772(0) 02(5) 73(0)

3(5) 6

Wednesday



Wednesday


Homework Reviewp. 46 #1p. 55 #8 p. 64 #14p. 68 #25*

Tuesday

Essential Question: How are Distributions Described Using Numbers?

Lecture/ Reading pp 69 – 74 (15 min)Discussion Problems #27, 40Mean vs MedianTech Toolbox p. 81


Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53


Tuesday


Measuring SpreadA.Quartiles

B.The Five-Number Summary & Box Plots

C.The 1.5 X IQR Rule for Suspected Outliers

Tuesday


Measuring SpreadD.The Standard Deviation

E.Choosing Measures of Center & Spread

F.Changing the Unit of Measurement

G.Comparing Distributions

Tuesday


Lecture/ Reading pp 69 – 74 (15 min)Discussion Problems #27, 40Describing Distributions w/ Numbers StationsTech Toolbox p. 81


Homework p. 74 #27 p. 89 #41, p.97 #49, p. 100 #53


Wednesday


Homework Reviewp. 74 #27 p. 89 #41p.97 #49p. 100 #53

Wednesday


Warm Up:

Standard: Describing patterns and departures from patternsExploratory 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

Wednesday


Displaying DistributionsA.Make an effective StemplotB.Make a histogramC.Make an ogive of a set of quantitative data


Wednesday


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.


Wednesday


Make an ogive of a set of quantitative data

Practice Problem p. 64 #1.14b

Wednesday


0 0 1 4 4 4 6 7 7 7 10 15What is a boxplot?

52 7

Wednesday


Why Use Boxplots?Boxplots help us to compare distributions side by sideThey also allow us to see the shape of the distribution

Five Number Summary & BoxplotsMinimum 1st Quartile Median 3rd Quartile Maximum min Q1 Q2 Q3 max

The Interquartile Range IQR Q3 – Q1

An observation may be an outlier if it falls more than 1.5xIQR above Q3 or below Q1

Technology Toolbox p. 81

Wednesday


Wednesday


Displaying DistributionsA.Make an effective StemplotB.Make a histogramC.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


Warm Up:

Thursday


Tonight’s Homework: p. 97 #1.47p. 102 #58 p. 110 #68 p. 111 #70

Thursday


Assessing Shape A.Look for overall patterns & for major deviations from patternsB.Determine whether or not the distribution is roughly symmetric, distinctly skewed, or neither. Look for modesC.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

Thursday


Mean Median

1. Found by ______________________and dividing by the number of Observations2. Known as the _________ value3. Sensitive to the influence of _______________4. Can be found using the _________5. Takes into consideration theValue of each _______________

1. Found by ____________the observations and choosing the__________ value2. The _____ percentile3. Resistant to _________ values4. Must be done by _______ or by_______________5. Only takes into consideration the ___________ of observations

Thursday


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 summaryE. Recognize Outliers IQR x 1.5

Thursday


The Effects of Mean & Median on the Shape of Distributions1. __________ If the mean = mode or they are very close to each other2._________ If the mean is further out in the tail than the median

Thursday


Comparing DistributionsThere are many ways to compare distributions:

Side by side boxplotsSide by side bar graphsBack to back stem-plots

Are just a few.Read page 94 - 96 starting with Example 1.19Do you feel comfortable deciding which comparison to use?

Thursday


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

Thursday


Wrap UpCongratulations! 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

FridayEssential Question:

How well do I understand how to explore data?Opening

Warm Up:

Homework Review

FridayEssential Question:

How well do I understand how to explore data?

MiddleGroup Assignments & PresentationsQuiz on Chapter 1

EndHomework Read 2.1 page 116 – 152 Outline the section

AP Statistics Unit I: Describing patterns and departures from patterns Week 6 MM4A1. Students will explore rational functions. b. Find inverses of rational.

Documents

study patterns

patterns week

numerical displays

categorical data

use of graphical

exploring data week

numerical techniques

exploring bivariate