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eBook Lesson for AP Stats
Content Area
AP Statistics
Title
Researching Famous Statisticians
Grade Level
High school students grades 10-12
Overview
Students are to further study a topic from the AP Statistics standards by learning about the person that invented, discovered or expanded the statistical idea. In teams of two students, once a statistician has been chosen to research, students should type their results into an eBook such as Mixbook. Students can either post all individual results into a single class eBook or each team of students can create their own eBook then post results onto a classroom website.
Time Frame
1-3 class periods depending upon the technology available to students both inside and outside of the classroom.
Materials
A list of statisticians for students to choose from. Highly recommend each pair of students choose different people.
A computer or tablet for each student.
Access to the Internet for Mixbook and Search Engines
Description of Lesson
Additional Lesson Details
To avoid duplicating statisticians, students could start a class list on Primary Pad, or add to a list written in the classroom. For example, list names alphabetically by last name for an easier search for duplicates.
To add quality to the eBooks, require students to have certain components included in their eBook such as:
Standards
College Board Standards for AP Statistics
Students may choose any statistician that has worked on any or more of the following topics.
Adapted from The College Board Internet Resources
I . Exploring Data: Describing patterns and departures from patterns (20%–30%)
Exploratory analysis of data makes use of graphical and numerical techniques tostudy patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries. 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 . Shape
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
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
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
II . Sampling and Experimentation: Planning and conducting a study (10%–15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
A . Overview of methods of data collection
1 . Census
2 . Sample survey
3 . Experiment
4 . Observational study
B . Planning and conducting surveys
1 . Characteristics of a well-designed and well-conducted survey
2 . Populations, samples and random selection
3 . Sources of bias in sampling and surveys
4 . Sampling methods, including simple random sampling, stratified random sampling and cluster sampling
C . Planning and conducting experiments
1 . Characteristics of a well-designed and well-conducted experiment
2 . Treatments, control groups, experimental units, random assignments and replication
3 . Sources of bias and confounding, including placebo effect and blinding
4 . Completely randomized design
5 . Randomized block design, including matched pairs design
D . Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys
III . Anticipating Patterns: Exploring random phenomena using probability and simulation (20%–30%)
Probability is the tool used for anticipating what the distribution of data should look like under a given model.
A . Probability
1 . Interpreting probability, including long-run relative frequency interpretation
2 . “Law of Large Numbers” concept
3 . Addition rule, multiplication rule, conditional probability and independence
4 . Discrete random variables and their probability distributions, including binomial and geometric
5 . Simulation of random behavior and probability distributions
6 . Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable
B . Combining independent random variables
1 . Notion of independence versus dependence
2 . Mean and standard deviation for sums and differences of independent random variables
C . The normal distribution
1 . Properties of the normal distribution
2 . Using tables of the normal distribution
3 . The normal distribution as a model for measurements
D . Sampling distributions
1 . Sampling distribution of a sample proportion
2 . Sampling distribution of a sample mean
3 . Central Limit Theorem
4 . Sampling distribution of a difference between two independent sample proportions
5 . Sampling distribution of a difference between two independent sample means
6 . Simulation of sampling distributions
7 . t-distribution
8 . Chi-square distribution
IV . Statistical Inference: Estimating population parameters and testing hypotheses (30%–40%)
Statistical inference guides the selection of appropriate models.
A . Estimation (point estimators and confidence intervals)
1 . Estimating population parameters and margins of error
2 . Properties of point estimators, including unbiasedness and variability
3 . Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals
4 . Large sample confidence interval for a proportion
5 . Large sample confidence interval for a difference between two proportions
6 . Confidence interval for a mean
7 . Confidence interval for a difference between two means (unpaired and paired)
8 . Confidence interval for the slope of a least-squares regression line
B . Tests of significance
1 . Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power
2 . Large sample test for a proportion
3 . Large sample test for a difference between two proportions
4 . Test for a mean
5 . Test for a difference between two means (unpaired and paired)
6 . Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables)
7 . Test for the slope of a least-squares regression line
21st Century Standards
Adopted from The Glossary of Education Reform
AP Statistics
Title
Researching Famous Statisticians
Grade Level
High school students grades 10-12
Overview
Students are to further study a topic from the AP Statistics standards by learning about the person that invented, discovered or expanded the statistical idea. In teams of two students, once a statistician has been chosen to research, students should type their results into an eBook such as Mixbook. Students can either post all individual results into a single class eBook or each team of students can create their own eBook then post results onto a classroom website.
Time Frame
1-3 class periods depending upon the technology available to students both inside and outside of the classroom.
Materials
A list of statisticians for students to choose from. Highly recommend each pair of students choose different people.
A computer or tablet for each student.
Access to the Internet for Mixbook and Search Engines
Description of Lesson
- Students choose a partner to work with.
- Students choose a statistician to research and submit to a class list to avoid duplicates.
- Students should research their chosen statistician using a search engine such as Google.
- Students should put all results into an eBook such as Mixbook.
- Wrap up the lesson by sharing the class's results either inside or outside of class.
Additional Lesson Details
To avoid duplicating statisticians, students could start a class list on Primary Pad, or add to a list written in the classroom. For example, list names alphabetically by last name for an easier search for duplicates.
To add quality to the eBooks, require students to have certain components included in their eBook such as:
- Title page - student names, date and statistician full name
- Introduction page - Provide a picture of the person, date of birth and death if applicable. Also provide some childhood background here.
- Schooling Page - What was school like for this person? Which schools did they attend? What degrees do they hold?
- Work Background Page - Name as many places where they worked as possible. State what they did and/or accomplished at each place.
- Statistical Information - Using 2-3 pages students should describe the statistic(s) their statistician is famous for. If more than one, list more. Provide all details possible about the statistic, it's applicability, it's development etc. Add something else that is creative and/or different from these instructions.
- Resource Page - Provide all Photo Credits and References Accessed.
- Pictures - Provide a picture on at least half of the book pages (minimum). One per page is ideal (extra credit).
Standards
College Board Standards for AP Statistics
Students may choose any statistician that has worked on any or more of the following topics.
Adapted from The College Board Internet Resources
I . Exploring Data: Describing patterns and departures from patterns (20%–30%)
Exploratory analysis of data makes use of graphical and numerical techniques tostudy patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries. 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 . Shape
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
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
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
II . Sampling and Experimentation: Planning and conducting a study (10%–15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
A . Overview of methods of data collection
1 . Census
2 . Sample survey
3 . Experiment
4 . Observational study
B . Planning and conducting surveys
1 . Characteristics of a well-designed and well-conducted survey
2 . Populations, samples and random selection
3 . Sources of bias in sampling and surveys
4 . Sampling methods, including simple random sampling, stratified random sampling and cluster sampling
C . Planning and conducting experiments
1 . Characteristics of a well-designed and well-conducted experiment
2 . Treatments, control groups, experimental units, random assignments and replication
3 . Sources of bias and confounding, including placebo effect and blinding
4 . Completely randomized design
5 . Randomized block design, including matched pairs design
D . Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys
III . Anticipating Patterns: Exploring random phenomena using probability and simulation (20%–30%)
Probability is the tool used for anticipating what the distribution of data should look like under a given model.
A . Probability
1 . Interpreting probability, including long-run relative frequency interpretation
2 . “Law of Large Numbers” concept
3 . Addition rule, multiplication rule, conditional probability and independence
4 . Discrete random variables and their probability distributions, including binomial and geometric
5 . Simulation of random behavior and probability distributions
6 . Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable
B . Combining independent random variables
1 . Notion of independence versus dependence
2 . Mean and standard deviation for sums and differences of independent random variables
C . The normal distribution
1 . Properties of the normal distribution
2 . Using tables of the normal distribution
3 . The normal distribution as a model for measurements
D . Sampling distributions
1 . Sampling distribution of a sample proportion
2 . Sampling distribution of a sample mean
3 . Central Limit Theorem
4 . Sampling distribution of a difference between two independent sample proportions
5 . Sampling distribution of a difference between two independent sample means
6 . Simulation of sampling distributions
7 . t-distribution
8 . Chi-square distribution
IV . Statistical Inference: Estimating population parameters and testing hypotheses (30%–40%)
Statistical inference guides the selection of appropriate models.
A . Estimation (point estimators and confidence intervals)
1 . Estimating population parameters and margins of error
2 . Properties of point estimators, including unbiasedness and variability
3 . Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals
4 . Large sample confidence interval for a proportion
5 . Large sample confidence interval for a difference between two proportions
6 . Confidence interval for a mean
7 . Confidence interval for a difference between two means (unpaired and paired)
8 . Confidence interval for the slope of a least-squares regression line
B . Tests of significance
1 . Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power
2 . Large sample test for a proportion
3 . Large sample test for a difference between two proportions
4 . Test for a mean
5 . Test for a difference between two means (unpaired and paired)
6 . Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables)
7 . Test for the slope of a least-squares regression line
21st Century Standards
Adopted from The Glossary of Education Reform
- Research skills and practices, interrogative questioning
- Creativity, artistry, curiosity, imagination, innovation, personal expression
- Perseverance, self-direction, planning, self-discipline, adaptability, initiative
- Oral and written communication, public speaking and presenting, listening
- Leadership, teamwork, collaboration, cooperation, virtual workspaces
- Global awareness, multicultural literacy, humanitarianism