  # AP Statistics Lessons with Mr. Tarrou

## Video Lectures

Displaying all 79 video lectures.
I. Introduction; Displaying Data
Lecture 1 Play Video
Stem Plots in Statistics
An introduction to the benefits, construction, and interpretation of stem plots.
Lecture 2 Play Video
Histograms in Statistics
Introducing the uses of histograms in statistics, how to construct them and interpret them.
Lecture 3 Play Video
Making histograms, boxplots,and timeplots with a graphing calculator
An introduction to making histograms and boxplots with the TI-83 and TI-84.
Lecture 4 Play Video
Catagorical Graphs in Statistics
An introduction to pie charts and bar graphs. I talk about their construction and the pros and cons of each type of graph. Please excuse my grammatical error on the third bullet under pie charts...catagory's relation.
II. Describing Distributions
Lecture 5 Play Video
Describing Distributions in Statistics
The four key points are discussed when describing distributions in statistics...Shape, Center, Spread, and Outliers. Please forgive the misspelling of DESCRIBED in the video.TIP to identify Left & Right Skewness: (Thanks LeBadman:) Left: Mean is less than Median is less than Mode Symmetrical: Mean, Median and Mode are approximately equal Right: Mean is greater than Median is greater than ModeYou just take: Mean, Median, Mode If it's left skewed, you will see the inequalities pointing to the left. If it's right skewed, you will see the inequalities pointing to the right.
Lecture 6 Play Video
Determining Skewness In Ogive Graphs
I help you identify left skewness, right skewness, and bell curves in an Ogive graph. At 6:40 I said "this is left skewed"- that is incorrect. Skewness is determined by the direction of the tail. In the histogram, the tail tapers off to the right, so it is right skewed.
Lecture 7 Play Video
Resistance, Mean, Median, 5 Number Summary and BoxPlots
I start going over 5 number summary of distributions, define resistance, and box plots.
III. Density Curves & Normal Distributions
Lecture 8 Play Video
Standard Deviation Preview and IQR Test
I overview the definition of standard deviaiton and introduce the IQR test in statistics.
Lecture 9 Play Video
Distribution Shapes, Ogive Graphs, and Time Plots
A review of the shapes of distributions and the relationships between the three measures of center. Also included is an intro to the Ogive graph and Time Plots.
Lecture 10 Play Video
Standard Deviation and Linear Transformations
An introdution to Standard Deviation, it's properties, and the linear transformation process. LINEAR TRANSFORMATION AT 9:01
Lecture 11 Play Video
Density Curves, Empirical Rule & Normality, Z-score Intro
I define density curves. I also define Normality through the Empirical Rule. We then introduce the Z-score formula, which is a linear transformation, and show how is allows us to use the Standard Normal Distribution to find p-values. DENSITY CURVES 0:04 EMPERICAL RULE 3:48 Z-SCORE INTRO 6:50 EXAMPLE 11:01 I have no idea what happened to the end of my lesson.  If you need help finding area under a bell curve you can check out https://www.youtube.com/watch?v=_86q-hn_3DQ&list=PLC84780005...
Lecture 12 Play Video
Normal Probability Plots & the TI-84
I show you how to make a Normal Probability Plot on your TI-83 or TI-84 calculator. We will see how this graph verifies normality and how it shows left and right skewness. You will also be reminded of how to view boxplots and histograms on the same screen shot to get used to comparing the two types of graphs.
Lecture 13 Play Video
z-score Calculations & Percentiles in a Normal Distribution
I show you how to calculate Z-scores and find areas under the bell curve...p-values. I will also show you how to find statistics from areas under the curve...such as quartiles.You can find p-values with a calculator as well. This is what it looks like on a TI-NSPIRE TI-NSPIRE Z score to Pval & Pval to Zscore NormCDF invNorm https://www.youtube.com/watch?v=-kmJRVr-ZQ8
Lecture 14 Play Video
TI-NSPIRE Z score to Pval & Pval to Zscore NormCDF invNorm
I show you how to get a p-value from a z score, and get a z score from a p-value using a TI-NSPIRE using the NormCDF(lower limit, upper limit, mean, standard deviation) command and invNorm(p-value, mean, standard deviation) command.
IV. Scatter Plots & Linear Regression Model
Lecture 15 Play Video
Scatter Plot Intro and Lurking Variables defined
I introduce the structure of scatterplots and explain what characteristics you will need to use to intrepret them. I discuss how lurking variables can help to form the patterns that we see. I also go over the two type of outliers we may see in scatterplots.
Lecture 16 Play Video
Intro of Corellation "r" to measure linear strength
I introduce correlation and how it measures the strength and direction of a linear relationship. I also discuss the many properties of correlation you must be familiar with. Coefficient of Determination is also defined.In the last example about MPG, r = -.8 and not positive .8 as written.
Lecture 17 Play Video
Outlier vs Influential Point
I compare the affects of an outlier and an influencial point on the regression line with the help of a TI-NSpire
Lecture 18 Play Video
Regression lines, Residual plots, and Correlation with TI-NSpire
I introduce the regression line and talk about some of it's key characteristics before showing you how to find it's equation with a TI-NSpire calculator.
Lecture 19 Play Video
Least Squares Regression Line Notes
I give notes of the concepts and properties of Least Squares Regression lines in Statistics, residuals, and preview minitab output.
Lecture 20 Play Video
Regression Lines and Correlation with TI-84
I make a scatterplot, calculate the Least Squares Regression Line, find correlation, and then make a Residual Plot to verify the linearity of the scatter plot.
Lecture 21 Play Video
Log Transformation Part 1
I introduce log transformations and show how to make curved exponential data linear so that we can analyze the data with a linear regression line. Part 2 is transforming data that follows a power function.
Lecture 22 Play Video
Log Transformations Part 2
I finish my log transformation introduction by introducing notes for Power Functions.
Lecture 23 Play Video
Log Transformations with a TI-NSPIRE
I create data from expontial and power equations, make scatter plots out of that data and then show you how to transform those plots so they are linear. This is known as log transformations in statistics.
V. Using of Graphing Calculator
Lecture 24 Play Video
Histogram, Boxplot, Dot Plot, & Normal Prob Plot on TI-NSPIRE
I show a quick video on entering univariate quantitative data in a TI-NSPIRE, and then I make a dot plot, histogram, box plot, and normal probability plot.
Lecture 25 Play Video
Scatter Plot, Linear Reg, Correlation & Residuals with TI-NSPIRE
I show you how to make a scatter plot, a least squares regression line, and a residual plot with a TI-NSPIRE
Lecture 26 Play Video
Log Transformations with TI-84
Log transformation demonstration with TI-84/83. This video will also review how to find least squares regression lines and making residual plots. I will also show how to remove the log function from your linear regression line to make either an exponential or power model for the original data.
VI. Introduction to Categorical Variables
Lecture 27 Play Video
I show an example of Simpson's Paradox. This is when an observed relationship is reversed when a third lurking variable is brought into the picture.Kidney Stone data referenced from: ^ C. R. Charig, D. R. Webb, S. R. Payne, O. E. Wickham (29 March 1986). "Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy". Br Med J (Clin Res Ed)
Lecture 28 Play Video
Relationship between catagorical variables in a 2 way table
I show you how to analyze catagorical data in a 2 way table. We will find marginal distributions, conditional probabilities, and bar graphs.
Lecture 29 Play Video
Log Tranformation with TI-NSPIRE
I go over how to to do a Log transformation with a TI-NSPIRE, explain how to determine the explanatory & response variable, and show how to remove the Log function to get a model for the original curved data.
VII. Evidence of Causation
Lecture 30 Play Video
Causation Defined & 5 Key Checks for Signs of Causattion
I defined causation, review the two types of lurking variables, and I go over the 5 checks for evidence of causation.
VIII. Sampling Techniques and Experimental Design
Lecture 31 Play Video
Sampling Techniques Part 1
I define and discuss the differences of observational studies and experiments. I then discuss the difference between a sample and a census, then introduce two types of sampling techniques that yield biased results...Voluntary Response and Convenience Sampling.
Lecture 32 Play Video
Sampling Techniques Part 2
I continue to introduce sampling techniques. In this video I go over Stratified Random Samples, Stratified Random Sample, Cluster Samples, and Multistage Samples.
Lecture 33 Play Video
Cautions about Sample Surveys, Causes of Bias, and Inference defined
I finish my three part introduction of Sample Surveys. In this lecture I define Undercoverage, Non-Response, discuss causes of Biased Results, define Inference, and preview Sample Distributions.
Lecture 34 Play Video
Sampling Techniques & Cautions (Full Length)
I define and discuss the differences of observational studies and experiments. I then discuss the difference between a sample and a census. I introduce two types of sampling techniques that yield biased results...Voluntary Response and Convenience Sampling. I discuss Stratified Random Samples, Stratified Random Sample, Cluster Samples, and Multistage Samples. I finish by defining Undercoverage, Non-Response, discuss causes of Biased Results, define Inference, and preview Sample Distributions.
Lecture 35 Play Video
Experimental Design Part 1
In part one of this lecture I cover basic definitions related to experiments, the 3 Principles of Experimental Design, and define Statistical Significance.
Lecture 36 Play Video
Experimental Design Part 2
I finish my lecture on Experimental Design with an introduction to Block Design, Matched Pairs Design, and Double Blind Experiments.
Lecture 37 Play Video
Simulation Notes for Statistics
I introduce the concept of simulations and explain how they can be used to answer difficult statistcs questions, save money, or time.
IX. Introduction to Probabilities
Lecture 38 Play Video
Intro to Probabilities in Statistics (Full Length)
An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc.
Lecture 39 Play Video
Intro to Probabilities Part 1
An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc.
Lecture 40 Play Video
Intro to Probabilities Part 2
An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc.
Lecture 41 Play Video
Intro to Probabilities Part 3
An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc.
Lecture 42 Play Video
General Probability Rules (Full Length)
I go over the General Addition and Multiplication Rules in Statistics. I show how a Venn diagram can help with the General Addition Rule. I also explain how we started to learn conditional probabilities when we did row and column percents in 2 way tables.
Lecture 43 Play Video
General Probability Rules Part 2
I go over the General Addition and Multiplication Rules in Statistics. I show how a Venn diagram can help with the General Addition Rule. I also explain how we started to learn conditional probabilities when we did row and column percents in 2 way tables.
Lecture 44 Play Video
General Probability Rules Part 1
I go over the General Addition and Multiplication Rules in Statistics. I show how a Venn diagram can help with the General Addition Rule. I also explain how we started to learn conditional probabilities when we did row and column percents in 2 way tables.
X. Discrete & Continuous Variables
Lecture 45 Play Video
Discrete & Continuous Random Variables (Full Length)
I define and compare the two types of Random Variables in AP Statistics...Discrete & Continuous. The formulas for finding the mean and standard deviation of a discrete random variables are introduced, and I also review the old mean and standard deviation formulas that the calculators does when you do 1 Var Stats. Many old concepts are reviewed in this video such as probability models, z-scores, normality, degrees of freedom, etc.
Lecture 46 Play Video
Discrete & Continuous Variables Part 1
I define and compare the two types of Random Variables in AP Statistics...Discrete & Continuous. The formulas for finding the mean and standard deviation of a discrete random variables are introduced, and I also review the old mean and standard deviation formulas that the calculators does when you do 1 Var Stats. Many old concepts are reviewed in this video such as probability models, z-scores, normality, degrees of freedom, etc.
Lecture 47 Play Video
Discrete & Continuous Variables Part 2
I define and compare the two types of Random Variables in AP Statistics...Discrete & Continuous. The formulas for finding the mean and standard deviation of a discrete random variables are introduced, and I also review the old mean and standard deviation formulas that the calculators does when you do 1 Var Stats. Many old concepts are reviewed in this video such as probability models, z-scores, normality, degrees of freedom, etc.
Lecture 48 Play Video
TI-NSPIRE Discrete Random Variable Mean & Standard Deviation
I show you how to find the mean and standard deviation of a discrete random variable with your TI-NSPIRE.
XI. Combining Means and Variances
Lecture 49 Play Video
Combining Means and Variance in Statistics
I review how linear transformations affect the mean, standard deviation, and the variance of data. I then introduce the rules for combining the means and variance of mutliple sets of data and finish with an example.
Lecture 50 Play Video
Combining Means and Variance Examples
I do two examples of z- score calculations that involve combining means and variance. EXAMPLES AT 0:30 8:20
XII. Binomial and Geometric Setting
Lecture 51 Play Video
Binomial Setting & Binomial Distribution in Statistics Pt 1
In a two part video I introduce the Binomial Setting and Distribution where x is defined as the number of successes. This lecture also includes the formulas and examples for of the Binomial Coefficient and the Binomial Probability Formula. I also go over how to use the binompdf(n,p,k) and binomcdf(n,p,k) commands in a calculator.
Lecture 52 Play Video
Binomial Setting & Binomial Distribution in Statistics Pt 2
In part 2 of my lecture about the Binomial Setting, I show how to set up a probability distribution function for a binomial variable when x is defined as the number of successes. I then introduce how to find probabilities of binomial events through Normal Approximation and compare this process with the exact values we get with binompdf and binomcdf from a calculator.
Lecture 53 Play Video
Geometric Setting & Distribution in Statistics
I introduce the Geometric Setting & Distribution in statistics and compare it to the Binomial Setting. This video includes setting up a PDF, examples of finding probabilities, and a non-example of a geometric setting.
XIII. One Sample Mean & Central Limit Theorem One Sample Proportions
Lecture 54 Play Video
Calculating 1-Var Statistics with a TI-NSPIRE
I show you how to calculate mean, standard deviation, and find the 5-number summary with a TI-NSPIRE and the 1-Var Statistics command.
Lecture 55 Play Video
Intro to Sample Mean Distribution and Central Limit Theorem
I introduce the Central Limit theorem and explain how it helps to set up the distribution of sample means. This video only discusses setting up the distribution of a one sample mean when given the population standard deviation. I hint of the upcoming topic of t-distributions
Lecture 56 Play Video
1 Sample Mean Z-Test Example
I work through a 1 sample mean z-test. I include the required checks for working with means, preview how to make a hypothesis statement, and compare how a z-score with means compares to a z-score test with a single piece of data.
Lecture 57 Play Video
Introduction of Sample Proportions
A set of notes to help you understand the Binomial Setting and how to set up binomial proportions.
Lecture 58 Play Video
Example of 1 Sample Proportion Z-test
I do multiple examples of Normal Approximation calculations of sample proportions. I also compare this process to using the binomcdf(n,p,k) commands in you calculator.
Lecture 59 Play Video
N-SPIRE 1 Proportion Z-Test Example
I compare how to work 1 sample proportion z-tests with Normal Approximation and with the TI-NSPIRE calculator
XIV. Understanding One Sample Confidence Intervals
Lecture 60 Play Video
Intro to Confidence Intervals & 1 Sample Mean z Interval
I introduce the concept of confidence intervals and finish with an example of a one sample mean z interval. A note about Margin of Error: The Margin of Error accounts for random variability, NOT sampling errors, non-response, or undercoverage, etc. EXAMPLE AT 16:50
Lecture 61 Play Video
1 Sample Mean t-Confidence Interval
I introduce the t-distribution and work through an example of a 1 Sample Mean t-Confidence Interval. EXAMPLE AT 9:34
Lecture 62 Play Video
Matched Pairs t Confidence Interval
I do an example of setting up a Matched Pairs Mean t-Confidence Interval. The sixth student's score was mis-copied and should be a 95 instead of a 92. Sorry for the small copy error.
Lecture 63 Play Video
1 Sample Proportion z Confidence Interval
I work through and example of setting up a 1 sample z confidence interval.
XV. One Sample Significance Tests & Power
Lecture 64 Play Video
Significance Hypothesis Test Intro & Matched Pairs t-Test
I introduce the basics of setting up a significance test, such as defining a null and alternative hypothesis, checking conditions, etc. I finish by working through an example of a matched pairs t-test. EXAMPLE AT 19:00
Lecture 65 Play Video
2 Sided Hypothesis Tests & Confidence Intervals
I explain the relationship between 2-sided significance tests and confidence intervals.
Lecture 66 Play Video
Type 1 Error Type 2 Error Power 1 Sample Mean Hypothesis z-Test
I define what Type 1 and Type 2 errors and do an example. I then introduce power and work through and example of finding the power of a 1 sample mean z-test and the probability of a Type 2 error. The x's in the first half of my Power example should have bars on top of them to represent sample means.
Lecture 67 Play Video
Power of a T Test 1 Sample Mean
I explain the differences of finding Power of a t-Test compared to Power of a z-Test.
Lecture 68 Play Video
Power 1 Sample Proportion z-Test (2 Sided)
I work through an example of finding power of a 1 sample proportion z test which is 2 sided.
XVI. Two Sample Significance Tests & Confidence Intervals
Lecture 69 Play Video
2 Sample Mean t-test & Confidence Interval
I introduce how to compare 2 means in statistics. I cover the goals of the comparison, the required conditions that need to be checked, robustness, how to combine means and variance, and give the formulas for z-test...t-test...and confidence intervals. I finish with a few examples. EXAMPLE begins at 22:48
Lecture 70 Play Video
2 Sample Mean Hypothesis t Test & Confidence Interval Example w/ TI-NSPIRE
I work through a 2 sample mean t-test and a 2 sample mean t-interval using a TI-NSPIRE. The video starts with a description of the setting, hypothesis statement, and conditions check. Why? Because the numbers out of your calculator mean nothing if you can't do the test in the first place!!!
Lecture 71 Play Video
2 Proportions Pooled Hypothesis z-test & Confidence Intervals
I introduce how to compare 2 sample proportions through the use of z-tests and confidence intervals. I finish with a 2 Sample Pooled z-test. EXAMPLES AT 11:09 21:28
XVII. Chi-Square Test
Lecture 72 Play Video
Chi Square Goodness of Fit Test
I introduce the Chi Square Goodness of Fit test and finish with two examples. EXAMPLES AT 5:10 15:55
Lecture 73 Play Video
TI-NSPIRE Chi Square Goodness of Fit Test
Using an excerpt from a previous video I show you how to do a Chi Square Goodness of Fit test with the TI-NSPIRE.
Lecture 74 Play Video
Chi Square Test for Independence & Homogeneity
I introduce the concept of the Chi Square Test on 2 Way Tables. I work through 2 examples. 1) Chi Square Test for Homogeneity of Populations 2) Chi Square Test for Independence EXAMPLES AT 0:10 3:24 10:36
Lecture 75 Play Video
TI-NSPIRE Chi Square Test on 2 Way Tables
I use an excerpt from a previous video to show you how to do a Chi Square Test on a 2 way table.
Lecture 76 Play Video
Chi Square Calculation by Hand
I work through a Chi Square test on a 2 way table without much aid from a calculator.
XVIII. Linear Regression t-Test and Confidence
Lecture 77 Play Video
Linear Regression t test and Confidence Interval Corrected
I introduce the Linear Regression t test and confidence intervals for the slope of a regression line.
Lecture 78 Play Video
Linear Regression t test and Confidence Interval
Corrected Version for iPad Viewers at http://www.youtube.com/watch?v=vWgKDhki5Sw&feature=share&lis... introduce the Linear Regression t test and confidence intervals for the slope of a regression line. On the third screen I miscopied the denominator in the formula of Standard Error about the Least-Squares Line. The denominator should be n-2 and not n. I have an annotation correction, but you will not see it without Flash like on an iPad.
Lecture 79 Play Video
TI-NSPIRE Linear Regression t-test & Confidence Interval of slope
I work through an example of doing a linear regression t-test with your TI-NSPIRE and making a confidence interval to estimate the true slope of a regression line. For some reason I didn't find it necessary to properly round the numbers on the screen as I read through my example of how to use this calculator.