Casio fx-7000G vs Casio fx-CG 50: A Comparison of Generating Statistical Graphs

Today’s blog entry is a comparison of how a histogram, normal distribution graphs based on statistical data, scatter plots, and linear regression plot are generated on Casio’s first graphing calculator, the fx-7000G (1985) and the most recent (as of this blog post), the fx-CG 50 (2016). For the curious, the SD2 and LR2 modes are the statistical plot modes of the fx-7000G.

The procedures for the fx-7000G are the same for the fx-6500G, fx-7500G, fx-8000G (and equivalents) and fx-6300G.

The procedures for the fx-CG 50 are the same for the fx-CG 10/20, the fx-9860G series, and fx-9750G series.

Single Variable: Histogram Graphs and Normal Distribution Graphs

The screen shots for this section uses the example data:

Rank #	Rank (List 1)	Frequency (List 2)
1	10	11
2	20	19
3	30	36
4	40	39
5	50	33
6	60	13

Histogram: fx-7000G

1. Enter SD2 mode by pressing [ SHIFT ] [ MODE ] [ × ]. Execute Cls to clear the graph screen and Scl to clear the statistical data registers.

2. There is no automatic zoom adjustment for statistical data on the fx-7000G. Observe the data and set the range accordingly.

3. Count the number of ranks. We have to set aside additional memory registers for the bars. Do this by pressing [ SHIFT ] [ MODE ] [ . ] (Defm mode) and entering the number of ranks. For the data set above, we will need 6 additional registers (Defm 6).

4. Enter the data by using the [x^y] key, which acts as the data entry (DT) key for this mode. The format for each point is: rank ; frequency.

5. Draw the bar graphing by pressing [Graph] [ EXE ]. In other words, run the Graph Y= command without any other arguments. The bar graph can be traced.

(Note: The range I used is: Xmin: 10, Xmax: 70, Xscl: 10, Ymin: 0, Ymin: 40, Yscl: 10)

Normal Distribution Graph: fx-7000G

1. Clear the graph screen by executing Cls.

2. Redo the range. The y-values will have a probability of 1 or less. I like to set Ymin to a very small negative value so that the graph won’t be at the bottom of the screen.

3. Draw the normal graph by pressing [Graph] [SHIFT] [ ↑ ] {Line} 1 [ EXE ]. The command line is Graph Y=Line 1. The normal distribution curve can be traced.

Don’t forget to reset the memory to Defm 0 (or the setting you had) when you are done. Allocating for extra memory registers reduces the amount of program steps available.

Histogram: fx-CG 50

On the fx-CG 50, everything is done through the Statistics Mode. We can use any list from List 1 to List 26, generate multiple data sets and graphs, and on the fx-CG 10/20 and fx-CG 50, the graphs are in color.

1. For this graph, listed the ranks in List 1 and frequencies in List 2. From the main menu, press [ F1 ] {GRAPH}, [ F6 ] { SET }, and either [ F1 ], [ F2 ], or [ F3 ] to choose the graph slot Graph1, Graph2, or Graph3, respectively. Set the Graph Type to Hist.

2. Exit the setup by pressing [ EXIT ], and next press the corresponding graph slot. We will be prompted for the start value (Xmin) and the width (size of the rank). Press [ EXE ]. On the fx-CG 50, we do not have to worry about the window ranges because the Statistics mode automatically zooms the window to fit the data. Nice! The histogram can be traced.

Normal Distribution Graph: fx-CG 50

1. From the main menu, press [ F1 ] {GRAPH}, [ F6 ] { SET }. Change the Graph Type to N-Dist.

2. Exit the set up and press the graph slot. Again, the window zooms to fit the curve. The normal curve can be traced.

Linear Regression: Scatter Plot and Linear Regression Plot

X: (List 1)	Y: (List 2)
-8	-10
-4	-6
-1	0
2	3
5	6
8	8

Scatter Plot: fx-7000G

1. Enter LR2 mode by pressing [ SHIFT ] [ MODE ] [ ÷ ]. Execute Cls to clear the graph screen and Scl to clear the statistical data registers.

2. Adjust the Range (viewing window) to fit the data.

3. Enter the data by using the [x^y] key, which acts as the data entry (DT) key for this mode. The format for each point is: x, y.

If the point occurs more than once, use the format x, y; frequency.

The scatter plot dynamically updates and is shown each time a point is added.

Linear Regression Plot: fx-7000G

The line fits to the equation y = A + Bx (A is the y-intercept, B is the slope).

1. Execute the command Graph Y=Line 1 by pressing by pressing [Graph] [SHIFT] [ ↑ ] {Line} 1 [ EXE ]. The line is then plotted and can be traced. Easy as that.

Scatter Plot: fx-CG 50

Execute the statistics mode and enter the data. Like the histogram and normal distribution plots, the fx-CG 50 automatically adjusts the window to fit the statistical data for the scatter plot and linear regression line.

1. For this graph, List 1 has the x data and List 2 has the y data. From the main menu, press [ F1 ] {GRAPH}, [ F6 ] { SET }, and either [ F1 ], [ F2 ], or [ F3 ] to choose the graph slot Graph1, Graph2, or Graph3, respectively. Set the Graph Type to Scatter. You have an option of selecting the shape of the markers of the point.

2. Exit the setup by pressing [ EXIT ], and next press the corresponding graph slot. The scatter plot will be shown and you can trace the points.

Linear Regression Plot: fx-CG 50

1. While we are on the scatter plot screen, press [ F1 ] {CALC}, then [ F2 ] { X }. We have a choice of two forms: ax+b (default) or a+bx. I chose a+bx to match the fx-7000G.

2. The regression equation, along with the intercept, slope, and correlation are shown. When ready, press [ F6 ] {DRAW}.

3. The regression line is drawn, and the line can be traced.

I hope you enjoyed the comparisons between the classic fx-7000G and modern fx-CG 50.

Until next time,

Eddie

All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Casio fx-991EX Classwiz Tips: Tables and Graphs

Casio fx-991EX Classwiz Tips:  Tables and Graphs

This week I am going to show some things that can be done with the Casio fx-991EX Classwiz.  

Believe it or not, the Classwiz can produce graphs of functions.   But not in the way we are used to.  

Generating Tables and Graphs

To generate a table, press [ MENU ], 9: Table.  The Classwiz will always ask for two functions f(x) and g(x).  The function g(x) can be left blank.

You are asked for:

Start:  minimum x value

End:  maximum x value

Step:  change of x

number of steps =  ceiling((End - Start) / Step)

The maximum number of steps for f(x) alone is 45, it gets reduced to 30 if both f(x) and g(x) are used. 

The table of values are displayed.

While the table is displayed, you can generate a graph by pressing [SHIFT] (QR).  This has the Classwiz generating a QR code.  You will need a QR reader, which you can use the Casio EDU app to read the code.

Once the QR code fits into the camera, you are given a link.  Below are examples of graphs:

I hope this week has been helpful in highlighting some of the features of the Casio Classwiz.   For the students in school, I wish you a happy and successful school year.

The next blog post will be on September 15, 2022.   Also, I am going to talk about HHC 2022 in Nashville.  

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Lists in Numworks - Version 19.2

Lists in Numworks - Version 19.2

Introduction

In Version 19,  lists were added as an object in the Numworks calculator.  We can define and name lists with any values that we want. Lists are designated by the brackets { }. 

*   The values can be real number, complex numbers, numbers with units, scientific constants, and combinations of those types.   What is not allowed in lists are strings and matrices.

*  The indexing of lists starts with 1.   We can call a list's elements by the parenthesis after the list name.  For example,  xlist(10) recalls the 10th element of the list xlist.

*  { f(k) }_k≤value generates a list of f(k) from k=1 to value, step 1.   The variable can be almost any variable you want, except e and i.  e is designated as the exponential constant (about 2.71828...) and i is designated as the imaginary number √-1.   The limits are strictly from 1 to value.

*  Once a user defined list is created, the individual values cannot be changed.   Furthermore, there are no augment or delete commands.  In this sense, user defined lists acts like tuples in Python.

*  Lists can be recalled in the Statistics and Regression apps.   The system named lists V#, X#, and Y# are updated accordingly.

* Defining a list of random values will always change the randomized values every time a user defined list is recalled.  

Please note that this is for Version 19.2.  

Screenshots are captured using the Numworks Emulator on July 10, 2022:  www.numworks.com/emulator

Note:  Casio fx-991EX Week - September 5, 2022 to September 9, 2022 

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP Prime: Graphs of Permutation and Combination

HP Prime:  Graphs of Permutation and Combination

Definitions

Permutation:

perm(n, x) = n! ÷ (n - x)!

Combination:

comb(n, x) = n! ÷ (x! × (n - x)!)

Combination with Repeated Choices allowed:

comb(n + x - 1, x) = (n + x - 1)! ÷ (x! × (n - 1)!)

For the following graphs, I use screen shots with the HP Prime Virtual Calculator.

Discrete Graphs  

Let n and x be positive integers.

Continuous Graphs

N is still a positive integer while x is a positive real number.   The factorial can be represent as the Gamma function as  x! = Γ(x+1).  

3D-Graphs

The variables  x and y take real values.

Eddie 

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Casio fx-CG 50: Double the Investment, Rule of 72, and Rule of 69

Casio fx-CG 50: Double the Investment, Rule of 72, and Rule of 69

Introduction

Are you familiar with the Rule of 72?   In finance, the Rule of 72 refers to a simple formula to determine approximately how many years it takes an investment to double in value.  

The Rule of 72 is an approximate formula, stated as:

n = 72 ÷ I

We can determine the actual time value of money formula (without periodic payment):

FV = PV × (1 + I ÷ 100)^n

where:

FV = future value

PV = present value

I = interest rate

n = number of years

Let PV = 1 and at double the investment, FV = 2.

2 = (1 + I ÷ 100)^n

Solving for n:

ln 2 = ln [ (1 + I ÷ 100)^n ]

ln 2 = n × ln [ (1 + I ÷ 100) ]

n = ln 2 ÷ ln [ (1 + I ÷ 100) ]

This is an exact calculation.  

There is another approximation, called the Rule of 69, and the approximation is this:

n = 69 ÷ I + 0.35

In Summary:

Exact Calculation:  n = ln 2 ÷ ln [ (1 + I ÷ 100) ]

Rule of 72:  n = 72 ÷ I

Rule of 69:  n = 69 ÷ I + 0.35

Comparison

A spreadsheet, generated using a Casio fx-CG 50, is shown for rates from I = 2% to I = 20% in increments of 1%.

The Rule of 72 is the most accurate at I = 8%, with an error of 6.4 × 10^-3.  At interest rate I ≈ 7.846871453, the Rule of 72 equals the exact calculation.    

When I < 7.846871453, the Rule of 72 over-estimates.  Other wise the Rule of 72 under-estimates.  

For I = 2 to at least I = 20, the Rule of 69 under-estimates, but the difference shrinks as I increases.  

Here is a graphical comparison for values of I = 5% to I = 15%.  

Source

Thomsett, Michael C.  The Real Estate Investor's Pocket Calculator 2nd Ed. AMACOM:  New York.  2018.  ISBN 9780814438893 (paperback)

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Casio fx-CG 50: Functions as Polar Graphs

Casio fx-CG 50:  Functions as Polar Graphs

Introduction

The function y = f(x) and equations in the form f(x,y) = g(x,y) can be transformed into its polar form by applying the transformations:

x = r cos Θ

y = r sin Θ

It can be a challenge getting the transformed equation in the form r = w(Θ), but it seems to work best where f(x,y) and g(x,y) are polynomials.   

The following are graphs generated with a Casio fx-CG 50:

Function, y(x):   green with connected line

Polar Function, r(Θ):  blue with dots 

Graphs

# 1:

y = x^2, r = sin Θ ÷ (cos Θ)^2 and r = 0

# 2:

y = x^3, r = ±√(sin Θ) ÷ (cos Θ)^(2/3) and r = 0

# 3:

y = 3x - 4, r = 4 ÷ (3 cos Θ - sin Θ)

General:  y = ax + b, r = -b ÷ (a cos Θ - sin Θ)

# 4:

y = 1/3 * (x - 4), r = -4 ÷ (3 sin Θ - cos Θ)

General:  ay = x + b, r = b ÷ (a sin Θ - cos Θ)

# 5:

y = ±√x, r = cos Θ ÷ (sin Θ)^2

# 6:

y = x^2 + x, r = tan Θ ÷ cos Θ - 1 ÷ cos Θ

# 7:

y = 1/x, r = √(1 ÷ (cos Θ sin Θ))

Eddie 

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Graph Gallery Series with GeoGebra

Graph Gallery Series with GeoGebra

The following graphs are from one to five terms of an infinite series of the form:

Σ f(n,x) from n = 0 to ∞

I use the GeoGebra online graphing tool, it is a great online, and free, graphing, mathematics, and geometry app.  Check GeoGebra out at https://www.geogebra.org. 

Enjoy!

Series 1: 

Σ( n * x ) from n = 0 to ∞

Series 2:

Σ( x^n * e^(-n*x) ) from n = 0 to ∞

Series 3:

Σ( x^(-n) ) from n = 0 to ∞

Series 4:

Σ( n * erf((n * x) / (n + 1)) ) from n = 0 to ∞

Series 5:

Σ( n * sin x + sin( x * n ) ) from n = 0 to ∞

Series 6:

Σ( x^(-n) * cos( x * n ) ) from n = 0 to ∞

One of my favorite pictures.  I used this as a wallpaper on my PC.  Eddie 

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

A Look at Some 1st Grade Common Core Problems

A Look at Some 1st Grade Common Core Problems

Common Core… Time to Dive In

My goddaughter is entering first grade this year.  We all heard of Common Core Mathematics.  My introduction to Common Core was an unfortunate one: a Facebook post where a student was marked wrong because a drawing wasn’t done correctly.  However, since Common Core in the United States is a reality and since I anticipate being asked for help with the math homework, I’m going to need to check out what is being taught in first grade. 

I’m going to highlight some types of problems that might be encountered in a first grade class. 

I want to thank A+ Plus Math Coach, link: http://www.aplusmathcoach.com for posting worksheets that cover Common Core math from grades K-5.  Most of the type of problems I will talk about in today’s blog post is based of these worksheets. 

Math Skills Emphasized

* Place Value, Tens and Ones

* Addition

* Subtraction

* Simple Graphs

* Counting

It would help if the student knows all the addition facts involving 0 to 10.  Yes, that addition table we memorized as kids is still helpful.

For a full list of skills (it’s a long one), click here:  http://www.corestandards.org/Math/Content/1/OA/

Counting Problems

Sample Problem 1:  How many balloons are in the box?

 This is fairly simple, we should count 12 balloons.

Other counting problems have students arranging objects into groups of ten when possible. 

Sample Problem 2:  Rhonda has six pieces of candy and Rita has eight pieces of candy.  How many pieces of candy do they have together?

Illustrated is the candy Rhonda (dark brown pieces) and Rita (tan pieces) have.  One exercise to have the student group the objects in tens when possible.  For this problem, we can have one group of ten pieces while four pieces are left over.  1 ten and 4 ones make 14. 

Adding and Subtracting

Most adding and subtracting problems should be straight forward.  As I mentioned before, it will help greatly if the student knows their addition tables.

Algebra, Without the Symbols

Some problems are presented as they come from first level algebra.  Instead of “Solve for X”, it’s “Solve for the blank space”.

Sample Problem 3:  Fill in the blank:  5 + ___ = 8. 

If the student knows their addition, the student would come up with 3 as the answer.  Sometimes, the problem states “You have 5 units.  How many units do you need to make 8 units?”

Sample Problem 4:  Think of the problem 8 + __ = 10 to solve 10 - ___ = 8.

“You have 8 units.  How many units do you need to make 10 units?”

“You have 10 units, how many units do you need to give away to have 8 units left?”

The answer to both questions is 2.  If someone finds a better way to explain this, please post this in the comments. 

Sample Problem 5:  The following sentence is false:  5 + 7 + 9 = 16.  Remove one of the numbers on the left to make the sentence true.

The goal here is to find the two addends in the sentence that add up to 16.  From the three possibilities:

5 + 7 = 12, no

5 + 9 = 14, no

7 + 9 = 16, yes

Since 7 and 9 are required, the 5 needs to be removed.

Doubles

One concept that may be introduced is the concept of additive doubles.  Simply put, the doubles are:

1 + 1 = 2	2 + 2 = 4	3 + 3 = 6	4 + 4 = 8	5 + 5 = 10
6 + 6 = 12	7 + 7 = 14	8 + 8 = 16	9 + 9 = 18	10 + 10 = 20

How can this come into play?  Some adding problems can be labeled as double plus one and double minus one. 

Sample Problem 6:  7 + 8

This can be seen as a double plus one problem. Note we can break the 8 into 7 + 1, then we have 7 + 7 + 1 (a double addition of 7). 

The thought process:

If 7 + 7 = 14 (double 7 fact)

Since 8 is 1 more than 7, add 1 to 14:

14 + 1 = 15.

An alternate strategy is the doubles minus one strategy. 

Start by recognizing that 8 + 8 = 16 (double 8 fact)

Since 7 is 1 less than 8, subtract 1 from 16:

16 – 1 = 15

This a strategy that facilitates mental math.

For video explanation of doubles, click on this link from Stephanie K:   https://www.youtube.com/watch?v=mbKkasLm5DY or from Bob Kowalec:  https://www.youtube.com/watch?v=elj4aup0wJk 

Graphs and Polls

I saw several problems that would require students to read graphs. 

Sample Problem 7:  Look at the table below, as a classroom of students in Mrs. Roberts said what their favorite toy is.  Mrs. Roberts tallies the results in the box below:

What is the most popular toy?  How many students participated in the poll?  (and similar questions)

This type of problem encourages counting and reading graphic representation of polls.  (Answers:  video game, 3 + 6 + 7 = 16)

Final Remarks

Other problems that I saw included requiring students to mentally add and subtract 10, and compare numbers between 10 and 99 using place value (compare tens digit first, then if they are the same compare the ones digit first). 

This is not going to be every problem that could be presented in a first grade Common Core math class, but I wanted to get an idea of what is taught in the classrooms.  I don’t know how much different first grade math is from today from when I was in first grade, which is 35 years ago. 

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.