Mr. Rogers - AP Statistics Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter 1 Distributions 2 N-Distribution 3 Regression 4 NL Regression 5 Data

Unit Plan Practice Test Practice Test Answers

Chapter 1: Distributions AP Statistics Standards I. Exploring Data: Describing patterns and departures from patterns (20% –30%) A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) Center and spread Clusters and gaps Outliers and other unusual features Shape B. Summarizing distributions of univariate data Measuring center: median, mean Measuring spread: range, interquartile range, standard deviation Measuring position: quartiles, percentiles, standardized scores (z-scores) Using boxplots The effect of changing units on summary measures C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) Comparing center and spread: within group, between group variation Comparing clusters and gaps Comparing outliers and other unusual features Comparing shapes
Objectives Class Start Up Distribute & discuss syllabi . Essential Question: How many numbers are needed to describe a complex event or object? State the difference between categorical and quantitative variables and give examples of each. Note: Categorical data is drawn only on bar graphs or pie charts Define distribution and state two key pieces of information require to produce a distribution. The pattern of variation of a single variable Quantitative data (numbers) Frequency--How often various values are expected State the 3 key ways a distribution can be described. Central tendency or center Spread or variability Shape Homefun (formative/summative assessment): Read "Statistical Thinking", section 1.1 and 1.2, work exercises 1.3 (p.7), 1.5 (p.10)	Activities   Lesson 1   Warm Up: Have each person describe themselves with 2 words and 2 numbers. Object: Complex objects and phenomenon are frequently described with a few numbers. How these numbers are produced is critical.   The Key Elements Design--the systematic way in which the data is collected Analysis--the systematic use of graphical and mathematical tools  to describe and evaluate the data Conclusions--the systematic manner in which inferences are drawn from the data Key Concept: What is a distribution? Purpose: Lay the foundation for describing a set of data. Interactive Discussion: Objectives Resources/Materials: Picture of histogram with various sized increments to illustrate the key weakness of histograms.
Essential Question: When using a number to describe a complex event or object is there a difference between using a single number and using a single data point? Ch1.2 Describing Distributions Name and define the 3 key measure of central tendency. Mean - numerical average Mean = Σxi / n    or Mean = ( x1+ x2 + x3 + ... + xn) / n Median - midpoint, 50% above, 50% below Mode - most common data point or highest peak Given a set of data determine the mean, median and mode. Define and ID outliers. Outliers are data points that are thought to belong to a different distribution, hence, any influence they have on the properties of a distribution causes errors. Data point not in distribution Gaps Outliers and skew are not the same thing. Skew is part of a distribution outliers are not. State which measure of central tendency is generally most influenced by outliers. Using the Mr. Rogers Rat Tail Rule, state whether a distribution is skewed left or right, high or low. Give examples of data that would tend to be symmetrical and data that would be skewed left or right. Easy Test - skewed left or skewed low Hard Test - skewed right or skewed high Normal Test - symmetrical Incomes - skewed right or skewed high   Homefun (formative/summative assessment): work exercises 1.69	Lesson 2 Key Concept: Central tendency and shape of a distribution.   Purpose: Lay the foundation for describing a set of data. Interactive Discussion: Objective Conclusions based on single or poorly chosen data point are statistically indefensible! -- these are called: Anecdotes   Conclusions unduly influenced by a single data point are statistically indefensible! --these data points are Outliers Individual Work: Find the mean, median, and mode in simulated sets of data with both odd and even numbers of data points. The Mr. Rogers Rat Tail Rule--FAQ Skewed distributions often look like a rat with a long tail. The tail points in the direction of skew. What gets skewed? The mean gets skewed or moved in the direction the rat tail points. Why does skew matter? For a skewed distribution, the mean is less representative of the bulk of the data points. What gets skewed very little? The median. It will be more representative of the bulk of the data points than the mean.
Stats Investigation: Investigation School Evaluation - time approx 3 class periods (individual work) Purpose: Determine if it is reasonable for 50% of all schools receiving a school report card to be scored below average. Instructions: Perform the simulation of school ratings using the Excel Spread Sheet provided. Questions /Conclusions: (see Excel spread sheet.)
Essential Question: Is there a difference between looking at tables of numbers and looking at plots or graphs of numbers? Make dot plots. Make histograms using the TI-83 calculator and in Minitab. State the key weakness of histograms (see "Four Histograms"). Understand the meaning of percentile. Example: if a score of 57 is at the 10th percentile then 10% of the observations or data points fall below a score of 57. Convert distribution data into a relative cumulative frequency graph (generally expressed in %), often called an ogive (see page 27). Note: Ogives are often drawn with the otherwise abhorrent connect the dots style.   Homefun (formative/summative assessment): read 1.2, work exercises 1.15, 1.17, 1.19 p. 24-31	Lesson 3 Key Concept: Central tendency, spread, and shape of a distribution must be visualized in order to analyze them.   Purpose: Lay the foundation for describing a set of data. Interactive Discussion: Objectives Individual Work: Given a set of data, make a dot plot on paper, make a histogram using the TI-83, and make a frequency plot on paper. Group Work: Using an ogive drawn on a white board, answer was Bill Clinton a young president (page 28)?
Essential Question: Can the type of plot influence the conclusions drawn and if so how can this be prevented? Stem and Leaf Plots Draw and interpret stem and leaf plots. Draw and interpret back to back stem and leaf plots . State why a time plot should always be used in an analysis of data. Virtually everything is a function of time. Homefun (formative/summative assessment):  prob. 1.21, 1.29, 1.31, 1.51	Lesson 4 Key Concept: All data varies with time. Stem and Leaf Plot   Purpose: Understand the reasons all data should be plotted against time.   Interactive Discussion: Objectives What can a stem and leaf plot reveal ? What variable is virtually everything dependent on? Seat Work: Draw stem and leaf plots both on paper and a histogram with  a TI-83 calculators using using hot dog data p. 59, prob 1.47.
Essential Question: Is there a difference between skew and outliers? Box and Whiskers Plots Calculate quartiles, Q1 and Q3. Interpret 5 number summaries. Low, Q1, Med.,Q3, Hi Find the IQR or interquartile range for a data set. IQR = Q3 - Q1 Draw a box and whiskers plot. State the Mr. Rogers Rat Whisker Rule for determining skew using a box and whiskers plot. Long whisker indicates direction of skew. State the % of the data expected in each whisker and in the box for a box and whiskers plot. 25% Homefun (formative/summative assessment): prob. 1.39, 1.47:	Lesson 5   Key Concept: Using box and whiskers plots to describe distributions   Purpose: Box and whiskers plots are an outstanding tool for communicating information about data in a straight forward manner Interactive Discussion: Objectives Individual Work: Draw box and whiskers plots both on paper and with TI-83 calculators using simulated data.
Essential Question: Why are outliers important? Modified Box and Whiskers Plot Identify outliers using a modified box and whiskers plot. Whisker's End = 1st data pt within 1.5 IQR of Q3 Outlier = data pt beyond the whisker's end Create box and whisker plots on the TI-83. Create and interpret parallel box and whisker plots on the TI-83 and in Minitab. Note that a box and whiskers plot cannot detect gaps, clusters, or multi-modes, but here's the problem with other types of graphs such as dot plots, stem and leaf plots, and histograms: the ability to detect patterns depends on the interval size. There's no perfect plot for visualizing distributions. Homefun (formative/summative assessment): prob. 1.55, 1.59:	Lesson 6   Key Concept: ID outliers using modified B&W plots   Purpose: The modified box and whiskers plots are an outstanding tool for identifying outliers. Interactive Discussion: Objectives Which type of plot(s) is(are) best at identifying outliers in a consistent manner? Which type of plot(s) is(are) best at identifying clusters? Which type of plot(s) is(are) best at identifying multiple-modes? Which type of plot(s) is(are) best at identifying gaps? Individual Work: Draw modified box and whiskers plots both on paper and with TI-83 calculators using simulated data.
Essential Question: Ideally, how many data points in a set of data are needed to characterize spread? Standard Deviation Calculate range. range = (highest) - (lowest) Write the mathematical definition for standard deviation from memory and explain its meaning.   Calculated from an entire population   σ =  [ Σ(xi - μ)2 / n ]1/2       Calculated from a sample   s =  [ Σ(xi - xbar)2 / (n - 1) ]1/2 The standard deviation is a way to express how much a typical data point differs from the mean but is calculated so that large deviations have more influence. State how standard deviation and variance are related. variance = (standard deviation)2 Calculate standard deviations by hand and with a calculator Note the difference between S and sigma. S = an estimate of a population's std dev based on a sample sigma = the actual standard deviation of a population Be as one with the 3 points about standard deviation in the magic box on page 51. State why the standard deviation is a better indicator of spread than range. Std dev uses all the data points, range uses only 2 pts. State an approximate relationship between range and standard deviation. (range roughly = 6 sigma.) Homefun (formative/summative assessment): work exercises 1.73	Lesson 7   Key Concept: Measuring spread - Range, standard deviation, and IQR   Purpose: Understand the pros and cons of various spread measuring techniques. Quantities represented as Greek alphabet symbols are considered true (known by Zeus). Quantities represented in our normal alphabet (known by mere mortals) are estimates of the ones represented as Greek alphabet symbols. Interactive Discussion: Objectives Individual Work: Calculate ranges, IQR, standard deviations, and variances both on paper and with TI-83 calculators using monthly temperature data from the Geenville - Spartenburg Airport.
Essential Question: What will changing the units of measurement do to measures of spread and central tendency? Linear Transforms What is a linear transform? (See p. 53). xnew = a + b∙xold Example: the linear transform to change from Celsius to Fahrenheit (ºF) = 32 + 1.8 (ºC)   State the effect that multiplying each number by a constant and/or adding a constant to each number in a data set has on the following: (This effect is important to know when changing the data points' units.)   (each data point) + a (each data point) * b mean (mean) + a (mean) * b median (median) + a (median) * b standard deviation no change (std dev) * b IQR no change (IQR) * b range no change (range) * b Q1 and Q3 (Q1) + a & (Q3) + a (Q1) * b & (Q3) * b Homefun (formative/summative assessment): work exercises 1.45, 1.55	Lesson 8   Key Concept: The effects of linear transforms   Purpose: Interactive Discussion: Objectives Individual Work: Calculate ranges, IQR, standard deviations, and variances  with TI-83 calculators using monthly temperature data in Fahrenheit from the Geenville-Spartenburg Airport. Repeat the process using the same temperature data converted to Celsius. Record the mean, median, standard deviation, IQR, range, Q1, and Q3 for both Fahrenheit and Celsius.
Essential Question: How can I make an "A" on the test? Distributions Review Work the practice test. Review the objectives. Correctly interpret 5 number summaries. Look over free response problems from previous years. Memorize the mathematical definitions of variance and standard deviation for samples and populations. Master the vocabulary (see example below). Descriptive Term Comments Central Tendency     Mean Sensitive to outliers & skew   Median good when outliers or skew present   Mode rarely used Spread     range Very sensitive to outliers & skew   variance Sensitive to outliers & skew   standard deviation Sensitive to outliers & skew   IQR good when outliers or skew present Shape     Symmetrical can have multiple peaks   Skewed left Skewed low, easy test   Skewed right Skewed high, hard test, income

The Practice of Statistics, Yates, Moore, McCabe