Statistics: Graphing under the normal curve

The class is trying to integrate graphing calculators.  One skill is graphing under a normal curve.  The first step is to draw a normal distribution curve on the graphing calculator..  The link above has the screen shots for each calculation.  Shadenorm shades the specified area.  The TI84 sequence is Shadenorm(lower bound, upper bound, mean, and SD).  The mean for a normal curve is 0 and the standard deviation SD is 1.  To shade the entire normal curve the sequence is Shadenorm(-1E99, 1E99, 1,0) or (-4,4,0,1)  -1E99 or 1-99 represents infinity or is the program on the TI84 for infinity.  I defined the area under a normal curve as having four SDs in either direction from the mean 0.  Left is designated with - and right is +.  These exercises for shading the area under the normal curve and using normcdf to calculate percentage  were very helpful

It took hours and hours to find useful information about how to graph the normal curve and shade under the normal curve.  The exercises are very useful because they have picture!  The information to the right of these screen shots of the shading are normcdf( and calculate percentages.  In order to shade areas under a normal curve you must have the normal curve defined in y=, the window set for X and Y,  before shading.  Once you have y= and the window settings, the sequence is shadenorm(lower bound, upper bound, mean, SD), such as shadenorm(-1E99, -1.67, 0, 1)  Remember to add the boundaries AND the mean (0 for the normal curve) and SD (1 for the normal curve).  The other step I forgot initially was ENTER.  I defined shadenorm( 1.67, 1E99, 0,1) and forgot to hit ENTER.  I kept entering GRAPH. 

Statistics:chapter two Describing Location in a Distribution

We started class by reviewing the Hamburger and Hank Aaron Home Run activities.  We calculated a five point distribution for each (min, max, Q1, mean, Q3) and also the IQR.

Began chapter two by reviewing 2.1 Overview.

Apologia Physics

Today we reviewed the test questions for Module 2.  Everyone got number 7 wrong.  The question asked was to calculate when two vehicles would collide head on if they were driving toward each other.  The key to solving the problem is to add their speeds together before calculating the time to travel the distance.  One student calculated the time for each vehicle to cover the compete distance between the two vehicles.  That did not take into consideration that the vehicles would collide before reaching the end the distance between them.  I assigned another problem from module 2 for the next class so we get more practice with this type of problem.

Apologia Physics: Module 2 Motion

The first thing we did today was to review definitions of speed, velocity, and acceleration with the calculations and shapes of the motion graphs.  The kids were assigned On Your Own problems from the book to do at home.  They bring these back completed; we spend time in class reviewing the problems that posed difficulties.  I made copies of the Chapter 2 test and distributed them.  Friday, we'll check the tests in class.  This is the basic class format: labs, exercises, On Your Own problems, and a test.

Statistics: Graphing and Histograms

Today, Deb led the Stats class.  She reviewed linear regressions and one variable stats  she introduced normal distribution graph, how to shade, and how to clear shading.  Then, she used this data for Utah and Florida--located in this packet to show the class how to create population pyramids as good examples of histograms.   BTW, population pyramids are key topics in Human Geography and AP Environmental Science.  The class discussed the implications.  For example, there will be more demand for infant diapers in Utah and adult diapers in Florida.  The point is to differentiate between a bar chart of M&M candy colors and a population pyramid double histogram.  One can draw a number of inferences regarding future growth, its shape, etc.  Below is an example from one of the kids.

Statistics: A little Graphing Calculator and Chapter 1

The kids have been working with the graphing calculator doing different exercises at the beginning of class.  The first week, the kids met with the Chemistry class to learn how to use the graphing calculator to model data. 

This week, my wife, Deb, reviewed histograms, box plots, and calcs the first five or ten minutes with the Statistics class.  One student, Angel, had a question about entering and calculating two variable statistics on the graphing calculator.  Deb showed the class how to specify which data and how the calculations are displayed on the calculator.

I'm following Mrs. Daniel's AP Stats Blog. The textbook is difficult to read as there are many terms, formulas, example calculations to be done.  I thought this was boring and it was difficult for me to determine what was important and reduce to a few pages of notes.  However, Mrs. Daniels, a teacher of AP Stats, has a blog which contains for each chapter: summary of terms, notes to present each major section of each chapter, activities for the students to complete, and a reference sheet to hand out which includes important terms, examples of graphs, and formulas.  I plan to present to the class Mrs. Daniel's presentation, have the students complete a couple of hands on activities, have them complete at home the overview questions.

Today, Friday Sept 19, we reviewed the chapter one overview which they had completed at home.  We reviewed the drive time calculation exercise including mean, median, and standard deviation for the students' commute time to class.  This is one exercise where we will calculate the standard deviation by hand and then in the graphing calculator.  I explained the difference between the standard deviation s (std dev for a sample) and omega (std dev for the entire population).  In the first calculation divide by (n-1) rather than n (where n is the number of data points) because of Beeson's correction.  Since we are typically using a sample, not the entire population, of data, the standard deviation is probably understated square of each variance from mean, then dividing by n-1 before taking the square root.

Statistics: Standard Deviation

Once Stats completes the M&Ms and Water labs, Rob is teaching standard deviation (SD).  The TI84 calculates SD.  Rob thinks the kids should calculate it manually once to understand variance and just what SD is.  Khan Academy has step by step instructions.  Rob is using How long does it take you to drive home from school? to review mean, median, and mode, while teaching SD.

Once he finishes this activity, I would like to do the Parking Lot Biodiversity Lab.  A biodiversity index examines variance in ecosystems.  Another activity for the kids is constructing Population Pyramids or histograms.  These two activities show kids how the stat activities are relevant to Ecology and Human Geography.  This activity, Power of the Pyramids is excellent.  Read the questions.  When I use these exercises, we always discuss the implications of countries such as Japan or in Western Europe with low fertility rates AND countries with high fertility rates.  My focus is on economic  implications, not birth control or ZPG.

This census population exercise comparing states and even cities is excellent.