$Class Table$ stat.gsp - The Statistics Sketchpad Teacher's Manual

Page Intro & Purpose

During the Spring 2025 semester, I taught Calc I and Stat I. The calc had recent support material, and the stat had substantial support material but it was "older." To supplement the statistics, I took the calc material and used it in a video.

Within & Between in the "Center & Spread" Video

Beginning at 11:23 minutes into the video, and ending at 15:46 of the video, I used "The cumulative impact of the function from a to b" found in ReimannSums.gsp to teach the probability of a score being within x standard deviations of the mean or to compute p( a < z < b). See the Teachers' Guide at "Reimann Boxes & Sums, and Integration" and also Probability Notes for Calc I and also use fX.f'X.f''X.intX.gsp.

That spreadsheet and 5 minute video clip was the genesis of this page and the spreadsheet. Enjoy.

About the sketch pad

It facilitates a visual and concrete, analytic and numeric, approach to topics in a Statistics I course.
It DOES NOT REALLY TAKE A DERIVATIVE. It uses [ f(x +.005) - f(x - .005)]/.01 as an approximation of the derivative.
It DOES NOT INTEGRATE. It uses sums of 32 Reimann boxes plotted to produce a plot of a cummulative curve.
It DOES NOT present an algebraic approach or deal with computation problems and solutions.
It focuses on the topics of uniform, standard normal, and normal distributions, stanines, between and within a interval, p(x < x.test), p(z< z.test), p(a < z < b), confidence intervals, alpha, p, hypothesis testing images.
It provides the calc I content to explain how the spreadsheet was constructed and the use of the term "cumulative function," as in cumulative probability, to facilitate use of the "Mother Tongue" rather than just "mathematics." See The Languages of the Math Classroom

All material on this site is free. (Please cite the source.) The sketchpads/resources from which this material is taken include Reimann.htm, limit.gsp, DerAnyFx.gsp, and ReimannSums.gsp.

Other Calc I material is found at: $calc1$ and , and $calc.fa25$ .

Other Stat I material is found at: and and and .

0 - toc, Table of Contents

Page Intro & Purpose
About this Sketch Pad
0 - Sketchpad toc, Table of Contents
1 - UNIFORM Distribution, n=8
2 - NORMAL, Standard Normal Distribution, n=32
3 - between & within
4 - STANINE - Standard Nine
5 - interval between, within, confidence interval about mean, drag a0
6 - cumulative PROBABILITY DISTR, type mu, sigma, a, b
7 - BACKUP p( a < x < b), type
8 - Reimann calc image - static
9 - Reimann calc image - movable
10 - Reimann calc by typing
11 - green dot plot anti
12a - HYPOTHESIS TEST mean = k
13 - standard normal backup
14 - slide
15 - cumulative standard normal z table
16 - hold

stat.gsp - The Statistics Sketchpad

1 - UNIFORM n=8
Links & Images: Distribution Cheat Sheet

Activities

Discuss the mean and standard deviation.
Determine the total area under the curve, the total probability.
Change a and b to examine change in p(x).
Show & discuss the "Show "Why this f(x)" hidden info/image.
Visit "Distribution Cheat Sheet" to see info on other distributions.

2 - NORMAL
Links: normal & standard normal paragraph
Images
Activities

Determine the probability a number is greater than the mean.

Determine the probability a number is less than the mean.

Determine the total area under the curve, the total probability.

3 - Between & Within
Links: TABLE f, f(x), f '(x), f " " (x) Between & Within, pg. 3; also
Activities: *

4 - STANINE
Links

5 - Confidence Interval

6 - cumulative area - PROBABILITY DISTR stat spreadsheet probabi;ity for calc I

7 - BACKUP p( x < z )
Links: Show height and area computation; Show midpoint coputation; Show g(x)
Activities: 1. Start w/g(x) = 0; 2. Ask can an area be negative?; * Show negative & positive areas.; * Show the left vs midpoint vs right turning negative as x is dragged.; 3. Ask how would increasing the number of boxes effect the area?; 4. Ask which is the best approach for computation & why?; 5. Reveal g(x) and discuss height.; 6. Change f(x), g(x), or both.; 7. N is small (so the differences in the 3 different sums is large).
Use the midpoint sum to answer this question.
As is, the sum is an approximation of the area under f(x) from a to b.
What is the result if one wishes the sum from b to a?

8 - calc STATIC, Reimann Sums Notes
Links: * ReimannSumNotes.pdf; * Reimann.htm including ReimannSums.gsp
Activities: * Discuss areas, summation meaning & format; * Perhaps go to links

9 - calc ACTIVE - Reimann Sums - Moving Boxes
Links: Hide/Show Boxes; Hide/Show g(x); Hide/Show left-hand sums; Hide/Show g(x); Go to ReimannSums.gsp
Notes: * Reimann.htm exists and is formated like this page and includes
ReimannSumNotes.pdf and ReimannSums.gsp; * The next page shows example of area and sum computation.
Activities: * Show boxes.; * Discuss and position left-hand boxes, right-hand boxes, midpoint boxes.; * Discuss the areas and sum of area of
left-hand boxes, right-hand boxes, midpoint boxes.; * Move boxes from picture.; * Change a and b and perhaps f(x).; * Show boxes and discuss areas.; * Move boxes from picture.

10 - calc ACTIVE: Calc I version of the Cumulative Probability Distribution; -- the calculus that makes this Sketchpad work
Links: Probability Notes for Calc I
This provides a summary of statistics and the normal probability distribution.; ReimannSums.gsp; ReimannSums.gsp Teachers' Guide
Activities: * Show function f(x, mu, sigma); * Show constant 1.; * Show constant 2.; * Play.

11 - INTEGRATION by dots
Activities: * Determine c

12a - HYPOTHESIS TEST mean = k

Activities: * Edit mu.test, sigma.test, a, b, sample.x.bar, sample.n.; * Choose either alpha or alpha/2.; * Edit a and b as directed to compute p-value.

13 - standard normal backup
Links: normal & standard normal paragraph
Images
Activities

Determine the probability a number is greater than the mean.

Determine the probability a number is less than the mean.

Determine the total area under the curve, the total probability.

14 - slide
Activities
Plot the points.

View/trace the antiderivative.

15 - cumulative standard normal z table

16 - Hold

12 - HYPOTHESIS TEST mean = k Probably found in Reimann.gsp
Notes: The plotted points are off by a constant. It is an indefinate integral.
Change the parameter "plus c" to adjust the plotted antiderivative points.
Links: * Show g(x) and height = h(x); * Show ordered pairs of plotted points.; * Show "Why plus c?"; * Show blue Suggested Functions box.
Activities: * Change the function as desired.; * Functions that fit on the screen are suggested.

Fa25 Office Footer $calc.fa25$ $[MC,i. Home]$ $asquared at MCC$ $[Words]$

$calc1$

The "Cumulative z-scores probability table" is found at: stat.xls spread sheet .

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