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.

Statistics: Intro to Graphing Calculator

Update!  Yes, we finished the M&M lab, graphed the data in a histogram and practiced several data sets!   Whooooo!  This seldom happens!  We finished the planned lessons.


The Chemistry class meets Tuesdays and Fridays this year.  Tomorrow, my husband, Rob, and I are doing another combined Chemistry and Statistics class to introduce experimental design and how to use the graphing calculator.  

First, we're using this graphing exercise to see if the kids can enter the data into the STAT function, turn on STAT PLOT, set the range, graph the data (depth and average temperature), calculate the linear regression, and overlay the line of best fit over the scatter plot data.  In other words, see if they remember our lesson from Tuesday.  Maybe.

Next, Rob and I are going to do this Statistics and Probability Lab with M&Ms.  He and I have 15 small cups of 50 gram samples of the candies, from a party-size bag of regular M&Ms.  Most of the M&M labs use individual bags of candies for each student.  The party-size bag was cheaper; so we weighed 50 g. samples before class.  

We decided to have a quick discussion about experimental design, hypothesis, and controlled variables before the lab.  Basically, the kids are going to predict which color M&M candy is the greatest percent in the candy sample (alternate hypothesis) or the percentages of each color are the same (null hypothesis).  This article explains how two companies produce M&Ms varies slightly by company. The percentages by color are in this article--for milk chocolate candies!  

We are going to give each child a cup with 50 grams of candies.  They will count the number of each color candy and calculate the percentage of each color in the cup.  Next each table of three kids will pool the data.  Finally, we'll pool and calculate the class data.  Next Tuesday, Rob is going to do two other exercises with the Statistics class, such as sampling with replacement and outliers.  Once we have the class data, the kids are going to graph it in the graphing calculators and produce histograms--bar graphs by color.  Yeah!  

What does this have to do with Chemistry?  Very little.  However, it will allow a brief discussion of experimental design and introduce the kids to the graphing calculator.

Statistics: From the beginning

At the beginning of class, Rob and I switched.  He monitored Chemistry and I taught Statistics how to create a stem plot or a box plot.  We entered data (2,4,6,8,10,12) into L1 of Stats, graphed the stem plot, calculated one variable (1 Var) statistics and used the TRACE function on the stem plot or box plot to locate the quartiles and median.  We repeated with new data (5,10,15, 20, 25, 30).  The short-cut to set the Window or Range is Zoom 9 for STAT functions.

We reviewed definitions for mean, median, mode, quartile, a five point summary, box plot, examples.  They drew a bar chart or histogram based on the data in the book.

Apologia Physics: Motion

The kids are working on several motion labs: Ramps and Balls, Go Pro with Hot Wheels Car, and Are You Speeding?  The introduction to Motion allows for experimentation.  Are You Speeding? uses Pasco Spark with the motion sensor.  The kids literally follow the Sparkvue lesson to learn how to collect motion data with a motion sensor.
On Tuesday, the kids did experiments with ramps and balls.  (The ramps are 4x6 boards cut into one meter lengths at Lowes.  The ball is a Pinkie ball.)  The object was to demonstrate average speed and acceleration.  They leaned one board against a book shelf.  The other board was placed on the floor at the base of the first board.  How could they measure the acceleration of the ball as it rolled down the ramp?  We do not have a radar gun to measure the instantaneous speed at the bottom of the ramp.  We approximated the top speed of the ball by measuring the time it took to cross the one meter board on the floor; the assumption being that the ball would not slow down significantly on the flat portion.  After we measured the elapsed time of the ball on the one meter board on the floor, we compared that to the starting speed, which in this case was zero, got the difference and divided by the time elapsed by the ball rolling down the ramp.   This was the acceleration experienced by the ball on the ramp.  It is crucial that the students calculate the acceleration by dividing the change in speed by the time and include all units of measure.  Acceleration is changed in speed divided by time.  Therefore if they set up the calculation correctly the resulting measure is meters per second squared.



The kids used Hot Wheels track with the Go Pro Hero and the Hot Wheels car to measure the same as above.  By observing the GoPro video, we could determine the speed by counting the frames of video recorded by the car covering the measured meter.  It helps to put some colored tape on the beginning and end of the measured meter of Hot Wheels track so one can see the beginning and end of the measured distance.  After counting the frames, one must look up the frames per second for the GoPro and convert frames to seconds.  We were not able to use the motion sensor to determine instantaneous speed but they had fun trying it.

We used the motions sensor to measure a student's walking back and forth.  This measures the displacement from the beginning point.

The assignment for Tuesday is to read all or module 2 and complete the on-your-own problems.

Apologia Physics: What did we do today?

Today, the class reviewed terms; we spent most of the class reviewing the 'on your own' questions and answers.  The kids are completing the first test at home.  Tuesday, I'll go over any questions.  We should be ready for Motion.  I have several fun labs.

Apologia Physics: Week One and Two

Friday, Week Two, the kids are going over their homework, the 'On your own' questions and taking a test for Module 1.

Here is an outline of the activities for Day One.  First, we did this physics math pretest.  It took all class period taking the test and reviewing the answers.  This is important information; one of the kids did not know how to convert units.  Next, the class did the Accuracy and Precision Lab and finally Bowling for Density.

This other density lab we did is It's all about Density from Flinn Scientific.  The kids determine if which method, volume by displacement or volume by geometry is more accurate.  The class can determine which method is more accurate by determining the density of a variety of objects and comparing the densities they derive with know values.  My wife and I both use this lab for Chemistry and Physics.  We use density blocks and have a set of mini cubes like these.  We use household objects: toy block, marbles, small balls, cylinders, etc.  The kids must use a variety of objects for the lab.  Some of the objects will not fit into the graduated cylinder---deliberately!  This is an opportunity to introduce percent error to the class.  Below are photos of the equipment.