THE GETTYSBURG ADDRESS Sampling and Sampling Distribution BASIL CONWAY AND BRADLEY BEARDEN Teacher Leader Academy Basil Conway IV
Beauregard High School AP Statistics Auburn University Colorado State University Bradley Bearden Dadeville High School AP Statistics Auburn University
THE GETTYSBURG ADDRESS When you think about the Gettysburg Address, what do you think of? Four score and seven years ago, our fathers brought forth upon this continent THE GETTYSBURG ADDRESS Find a sample of 5 representative words from the Gettysburg Address (the
population). Write these words in the table. Count the number of letters for each word and record in the table. Do you think your five words were representative? CREATE A DOTPLOT OF YOUR 5 WORDS ON YOUR
PAPER Observational Unit: The number of letters Variable: A word in the Gettysburg Address Type: Quantitative FIND THE AVERAGE SIZE OF YOUR 5 WORDS
Write this in part d. CREATE A CLASS DOTPLOT OF YOUR AVERAGE Observational Unit: Averages Variable: Different peoples random 5 word length average Type: Quantitative
THE DIFFERENCE IS The distribution of a sample and a sampling distribution WHATS THE REAL AVERAGE SIZE WORD? 4.295 = population average How well did we do?
Were we biased? In which way? Why did this happen? SUGGESTED SAMPLING TECHNIQUES?
Would anything be helpful to complete these procedures? RANDOMLY PICK 5 WORDS Complete portions m o Use the dotplot at the board to complete question o. HOW DO THE SAMPLING DISTRIBUTIONS OF SIZE 5 COMPARE TO THE TRUE
POPULATION AVERAGE? One of the major points of statistics is to use a sample to adequately predict a population parameter. When this happens, we call the statistic and sampling procedure unbiased. COMPLETE PARTS R-T Use the dotplot at the board for question t.
COMPARE PARTS O AND T AT THE BOARD By comparing the two sampling distributions of size 5 and 20, how does sample size affect a sampling distribution? http:// www.rossmanchance.com/applets/OneSample.html?population=gettysburg
WHERE DOES THIS FIT IN THE ACCRS? In Grade 7, instructional time should focus on four critical areas. . (4) drawing inferences about populations based on samples. Understand that statistics can be used to gain information about a population by examining a
sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Algebra Represent data with plots on the real number line (dot plots, histograms, and box plots).
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets Pre-Calculus Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Use data from a sample survey to estimate a population mean or proportion; develop a margin
of error through the use of simulation models for random sampling. HOW DOES THIS CONNECT TO STATISTICS Central Limit Theorem Statistical Testing WHERE DO THE
MATHEMATICAL PRACTICE STANDARDS FIT? Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure.
Look for and express reg