Eddie's Math and Calculator Blog

Spotlight: Calculated Industries QR Calc <Title>

Quick Facts

Model: 3375

Name: QR Calc

Company: Calculated Industries

Timeline: 1993

Type: Quality Control, Statistics

Operating System: Algebraic

Digits: 7

Memory: 1 general purpose memory register plus specific variable registers 

Power: 1 CR-2032 battery

When I purchased the QR Calc, there was no manual with it. Normally, it wouldn’t present any issues because I can often find manuals online. That is not the case with the QR Calc. If there is any manual online, please email me. I’ll have to be more careful next time.

I apologize that I will not be able to describe all the functions but hopefully I describe enough features to give the reader a general idea. Please check out the sources below.

Features

Let’s start with the mathematical functions included: powers and roots (y^x, x². √), natural logarithm (ln), exponential function (e^x), reciprocal (1/x), arithmetic (+, -, ×, ÷), and the standard percent key which operates they people expect it to (%). The order of operations is enforced. Like a lot of calculators, the change sign (+/-) key is a shifted function.

The operating range of the calculator is 7 digits: -9,999,999 to 9,999,999. Any calculator that has a result outside of this range causes the QR calculator to display an error message.

The store key for the QR Calc is labeled [ Set ].

The function →PPM changes any number into n parts per million.

Example: 0.0014 →PPM displays 1,400 PPM.

Here are some functions I was able to find out and figure out:

Normal Distribution

The normal distribution functions calculate areas of the standard normal distribution, assuming that μ = 0 and σ = 1.

n [ nZ ]: lower tail probability (from -∞ to x = n)

n [ 2^nd ] (ModZ): probability from x = 0 to x = n

One Variable Statistics

The QR handles a single set of statistics with the following key and key sequences:

[ Add ]: Add a data point (Σ+)

[ 2^nd ] [ Add ] (Subtract): Subtract a data point (Σ-)

[ 2^nd ] [ + ] (S←→P): Toggle between standard deviation and population deviation (σn indicator)

[ x-bar ]: Calculate the arithmetic mean.

[ R ]: Calculate the range of the data.

[ 2^nd ] [ x-bar ] (N): Calculate the number of data points.

[ 2^nd ] [ R ] (σ): Calculate the deviation, depending on the deviation mode set.

[ Low ]: Returns the minimum value of the data set entered.

[ 2^nd ] [ Low ] (High): Returns the maximum value of the date set entered.

[ Skew ]: Skew. I’m not sure what formula the QR Calc uses because I have not been able to match results with any formula I found yet.

[ 2^nd ] [ Skew ] (Kurt): Excess Kurtosis. Kurtosis measures how concentrated the data is with respect to the mean.

The formula used for Excess Kurtosis:

μ4 = 1/n * Σ((xi – mean)^4)

kurtosis = μ4/s^4 – 3

Process Capability Indices

If a process is mature, that is a process that is regular and has been executed for a period of time, we can measure the capability index.

There are two capability indices:

Cp: for a centered analysis

Cpk: for a non-centered analysis. This metric is used for potential future performance.

Generally, we want these indices to be at least 1. Capable processes have an Cp index of 1.33 or higher.

Key strokes:

Enter the mean: [ Set ] [ x-bar ]

Enter the deviation: [ Set ] [ 2^nd ] [ R ] ( σ )

Enter the lower specification limit (based on the normal distribution): [ Set ] [ LSL ]

Enter the upper specification limit: [ Set ] [ 2^nd ] [ LSL ] (USL)

Each variable entered will have an indicator.

Calculate Cp: [ 2^nd ] [ Cpk ] (Cp)

Calculate Cpk: [ Cpk ]

Example:

LSL = - 1, USL = 1, mean = 0.05, deviation = 0.27

[ 2^nd ] [ × ] (AC) to clear out the registers if needed

0.5 [ Set ] [ x-bar ] (x-bar indicator is on)

0.27 [ Set ] [ 2^nd ] [ R ] ( σ ) (σ indicator is on)

1 [ 2^nd ] [ - ] (+/-) [ Set ] [ LSL ] (L indicator is on)

1 [ Set ] [ 2^nd ] [ LSL ] (USL) (U indicator is on)

Results:

Cp: 1.234568

Cpk: 1.17284

That is a pretty good process.

Formulas Used:

Cp = (USL -LSL) / (6 * σ)

Cpx = min((x-bar – LSL) / (3 * σ), (USL – x-bar) / (3 * σ))

Control Charts

We get to the main feature of the QR Calc: Control Charts and Capability Limits. On the back of the calculator, the QR Calc has a list of handy formulas.

The heart of the QR Calc is the table of constants that are used in control charts and limit charts. Often the chart limits are built on many samples of n data points each, where x-bar is the average of the sample averages, and R is the average of the range samples. We can also build chart limits with one sample. The QR Calc can only handle sample sizes from 3 to 25 data points.

Mean Control Chart Limits:

Lower: LCL-mean = x-bar – n * A2 * R

Upper: UCL-mean = x-bar + n * A2 * R

R Control Chart Limits:

Lower: LCL-R = n * D3 * R

Upper: UCL-R = n * D4 * R

A2, D3, and D4 are constants used in calculating control chart limits. Accessing these constants takes one argument, which is the sample size.

The A2 constant for a sample size of 3: 3 [ nA2 ] returns 1.023.

Below is a short table of constants, as determined by the QR Calc.

Sample Size n	Constant A2	Constant D3	Constant D4
5	0.577	0	2.114
10	0.308	0.223	1.777
15	0.223	0.347	1.653
20	0.18	0.415	1.585
25	0.153	0.459	1.541

Standard deviation can be estimated by using the average range ( R ) and another constant d2:

σ ≈ R / d2

Sample Size n	Constant d2
5	2.326
10	3.078
15	3.472
20	3.735
25	3.931

A table of constants from n = 2 to 25 can be found here:

https://sixsigmastudyguide.com/x-bar-r-control-charts/

Example:

Construct mean and range charts from a sample (n = 5):

3.995

4.26

4.37

4.44

4.58

Keystrokes:

(after clearing data)

3.995 [ Add ] 4.26 [ Add ] 4.37 [ Add ] 4.44 [ Add ] 4.58 [ Add ]

X-bar chart:

LCL: [ x-bar ] - 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 3.991455

UCL: [ x-bar ] + 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 4.666545

R chart:

LCL: 5 [ 2^nd ] [ nD4 ] (nD3) [ × ] [ R ] [ = ] Result: 0

UCL: 5 [ nD4 ] [ × ] [ R ] [ = ] Result: 12.36669

The QC calc has contains the E2 constant.

Final Thoughts

The functions that I still do not know about or have figured out are: TRGa, TRGb, RS a, RS b, %Low, and %High.

This review is incomplete. I will keep searching for a manual, I may have to buy another QR Calc.

This calculator is a rarity, and one worth checking out.

Sources

Hessing, Ted. “Process Capability (Cp & Cpk)” 6σSTUDYGUIDE.COM (no specific date give, first comment on November 19, 2014) https://sixsigmastudyguide.com/process-capability-cp-cpk/. Accessed January 2025.

Hessing, Ted. “X Bar R Control Charts” 6σSTUDYGUIDE.COM (no specific date give, first comment on April 17, 2018) https://sixsigmastudyguide.com/x-bar-r-control-charts/. Accessed January 2025.

Hewlett Packard. HP-65 Stat Pac 2 Cupertino, CA. https://literature.hpcalc.org/items/975 1975

Next time, I’m going to see if a manual comes with it. Not everything has a manual online.

Eddie

All original content copyright, © 2011-2025. 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.

Spotlight: Casio fx-92 Collège

Quick Facts

Model: fx-92 Collège

Company: Casio

Timeline: 2023-present

Type: Scientific with Algorithm programming, 10 digits, Algebraic with Text Writing

Memory: 9 variables (A-F, x, y, z), 900 bytes for a script space

Power: 1 AAA battery

The fx-92 Collège is a scientific calculator designed for French school students. The calculator keys, functions, instructions, and commands are all in French. I purchased this calculator from a Swiss vendor online. The fx-92 Collège is sold in France, and I wish it was sold worldwide.

Modes

The fx-92 Collège has these following modes:

Calcul	Calculate Mode: This is the regular calculator mode. The input and output can be set to 2D input/output or linear. The 2D input/output shows mathematical calculations as they are written naturally. Also, fractions, terms of pi (π), and exact square roots (collectively known as QIRAC) are shown in 2D mode.
Stats	Statistics Mode: 1 and 2 statistics mode. The regression offered is linear regression.
Tableur	Spreadsheet: 45 rows x 5 columns. The spreadsheet has a capacity of 2,380 bytes.
Tabl fonct	Function Table: up to 2 functions, f(x) and g(x)
Équation	Equation Mode: Linear systems of orders 2, 3, or 4
Prod. croix	Ratio mode: Solve for X A / B = X / D A / B = C / X
Algo	Algorithmique: Algorithm Mode. This is the programming mode.
Math Box	Math Box: This features four applications: Lancer de dés: Dice Roll (up to 3 dice, up to 250 rolls of the dice) Pile ou face: Coin Toss (up to 3 coins, up to 250 coin tosses) Droite grad.: Graph line intervals, up to 3 (x<a, x≤a, x=a, x>a, x≥a, a<x<b, a≤x<b, a<x≤b, a≤x≤b) Cercle: Circle app (trigonometric circle, semi-circle, hourly clock (Horloge))

The fx-92 Collège is part of the Casio’s Classwiz series (think fx-991CW and the international fx-82CW). The calculator has a back button, four direction keys, an [ OK ] button, a button acts like a scroll button. The home button (ACCUEIL) calls up the modes while the configuration (CONFIG) shows the set up options.

The calculator uses a comma as a fraction indicator instead of a decimal point to align with how numbers are written in France.

In France, the approximation of √92 is written as 9,591663047.

In the United States, the approximation of √92 is written as 9.591663047.

Mathematical Functions

Some of the featured functions are:

Euclidean division: |-. [ SECONDE ] [ ÷ ]. This function returns the quotient and remainder.

Example: 2025 |- 47 returns Q = 43; R = 4

Last Answer: [ Rép ]. This is the returns the last answer processed by the previous calculation. This is often labeled elsewhere as Ans.

Fraction Simplification: Simp. [ SECONDE ] [ Rèp ]. Simplifies fractions and rational expressions or attempts to give a fraction representation of a decimal.

Example: .5757575757575757 >Simp returns 19/33.

Logarithm and Natural Logarithm: These are not on the keyboard, but instead found in the CATALOG – Analyse fonction menu.

Exponential Function (e^x): The Euler constant (e ≈ 2,718281…) is found by pressing [ CATALOG ], [ ↑ ], selecting Autre (Other) and selecting e.

Catalog-Probabilitè:

%

Factorielle (Factorial: n!)

Permutation (nPr)

Combinasion (Combinatio: nCr)

Nombre alèatoire (Random Number, Ran#)

Entier alèatoire (Random whole number, RandInt#(low; high))

Note arguments are separated by a colon. (;)

Catalog-Calcul numérique:

PGCD: Greatest common divisor (GCD)

PPCM: Least common multiple (LCM)

Valeur absolue: Absolute value (abs, |x|)

Tronc. À l’unité: Shown as Ent when called, this is the integer part function.

Arrondi: Rounds the number to the fix mode settings

Partie entière: The greatest integer less than x.

Arrondi(;): Rounds the number to any number of decimals.

Example: Arond(π; 4) returns 3927 / 1250 = 3,1416

Catalog-Angl/Coord/Sexag…:

This sub menu has angle designations (x°, x^r (radians), x^g (gradients), polar/rectangular conversions, markers for degrees/hours-minute-seconds calculations).

Catalog-Trigonométrique:

All the trigonometric (sin, cos, tan) functions and their inverses. These six functions are already on the keyboard.

Algorithmique Mode: Algorithm

This is the fx-92 Collège’s programming function. There is one program space, which allows up to 900 bytes of memory. Each command takes at least 4 bytes of memory. The language is similar to Scratch.

The output screen is a split screen. On the top, a graph and drawing screen. The dimensions of 191 pixel wide, 48 pixel height. The graph dimensions are x = [-95,96] and y=[-24,24]. Draws can leave the screen, up to ±999. At the bottom is one line where numerical results and per-programmed messages are shown. Below is a table of the commands that are available:

(Créer un algorithme: Create an algorithm)

French	English	Function
Avancer de n	Move forward n	Move the point n points/pixels
Tourner de ⟲ Θ	Turn from ⟲ Θ	Rotate the arrow Θ degrees
S’ orienter à Θ	Orient yourself to Θ	Turn the pointer to angle Θ
Aller à x; y	Go to x; y	Move pointer to point (x,y)
Stylo écrit	Pen writes	Put the pen down to write
Stylo relevè	Pen raised	Raises the pen to stop writing
Metire var á (Shown as expression → var)	Set var to (Shown as expression → var)	Makes a calculation and sets it to a variable A – F, or z.
Demander valeur (Shown as ? → var)	Ask for a value (Shown as ? → var)	Prompts for a value to be stored in A – F, or z
Commenataire (shown as one of four comments)	Comment out of four per-programmed strings	“Oui” Yes “Non” No “Nombre?” Number? “Résultat :” Result : Pauses execution
Afficher résult var	Show result var	Shows the contents of a variable and pauses execution
Style	Style (Style of Cursor)	Fléche: Arrow Croix: Cross
Attendre	Pause	Pause execution of script
Répéter n ( ↑ )	Repeat n ( ↑ )	Repeat loop, n time (up to 10,000 times). Loop ends at ↑.
Répéter jusqúa cond	Repeat until cond	Repeat a loop until condition cond is met. =, ≠, >, <, ≥, ≤ are present in the CATALOG-ALGO menu
Si Alors (Fin)	If Then (End)	If-Then structure. =, ≠, >, <, ≥, ≤ are present in the CATALOG-ALGO menu
Si Alors Sinon (Fin)	If Then Else (End)	If-Then-Else structure. =, ≠, >, <, ≥, ≤ are present in the CATALOG-ALGO menu

Algorithms start with the pointer at (0, 0) and the pen up. The pointer first starts at angle Θ = 0° (right along the x-axis).

The angle Θ is only accessed in this mode, [CATALOG], Algo, Θ (and only in certain prompts).

The variables x and y refer to the pixel coordinates. They cannot be stored or asked for in this mode.

With each command, you get a prompt screen to fill in the inputs.

When the script pauses, press [ OK ] to continue.  

Also with OUTILS (options):

French	English
Copier & Insérer	Copy & Insert (at Paste)	Press [ OK ] to insert the line.
Insérer linger	Insert Row	Press [ OK ] to insert the line.
Tout supprimer	Delete the Script	To delete a line, press [ ←x ] instead.

The fx-92 Collège is the second Casio calculator to have this type of algorithm mode. It succeeds the fx-92+ Spèicale Collège.

Next Sunday, February 16, we will explore the differences between the fx-92 Collège’s algorithm program and the Turtle module in Python.

Final Thoughts

The algorithm is erased when the calculator is turned off. I wish this wasn’t the case but I can see why the calculator does not retain programs. The fx-92 Collège is designed for teaching basic coding. This is the reason I would like to see this model available readily worldwide, as I think it would sell well. Even though the target audience are middle school students, I think this calculator can be enjoyed by everyone, at any age.

My only gripe: why aren’t the logarithm (log, ln) and exponential (e^x) functions on the keyboard? I get that middle school students probably don’t work with these functions, but the fx-92 Collège is a scientific calculation, and it is customary to have these functions on the keyboard. Not a deal breaker in any stretch of the imagination, just a minor thing for me. I’m glad they are there.

If you get a chance to get this calculator at a reasonable price, buy it. Now I can hope that the AAA battery is used is a universal AAA battery, I probably will have to invest in metric small screwdrivers when it comes time to replace the battery.

Eddie

All original content copyright, © 2011-2025. 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.

Spotlight: Casio DF-320TM

Just the Facts

Model: DF-320TM

Company: Casio

Type: Desktop

Number of Digits: 12

Display: 3 lines

Power: Solar plus backup battery, LR 44

Years of Production: My guess is somewhere in the 2000s

Several months ago, I found this calculator at a thrift shop in Montclair, California for a $1.35 (after discount). The DF-320TM is a nice desktop calculator with three lines. The top two lines are used for specific purposes, while the bottom on line has general calculation and results on the third line.

Features

The features of the DF-320 TM include:

* 12 digit display. For those of us working with large numbers, the extra digits are nice.

* Two slide settings that are found on desktop calculators: rounding and the fixed decimal settings. Add mode is available for those who are proficient with adding machines or those who like working with dollars and cents without having to enter the decimal point.

* Cost/Sell/Markup calculation

* Sales tax and discount

* Exchange rate calculations between two currencies

* An [ H/M/S ] button which allows for hours-minutes-seconds calculation.

* Tracking of grand total every time when the equals key ( [ = ] ) is pressed. The grand total is retrieved by pressing the [ GT ] key.

* Determining change with the [ CHANGE CAL ] button.

All examples have the following setting: 5/4 rounding fixed to 2 decimal places.

Cost/Sell/Markup

The three keys, [ COST ], [ SELL ], and [ MAR ] (MAR for Markup) solve cost-sell-markup problems. Entries are made on the top screen and solving for the third variable occurs automatically.

Example:

1200 [ COST ] 12 [ MAR ]

Display:

COST> 1,200.00

MAR> 12.00%

= 1,363.64 (selling price)

Setting Tax and Exchange Rates

The DF-320TM employs the traditional way to set tax rate and currency exchange rate.

1. Start by pressing and holding [ AC ] and [ % ] until the screen reappears with the SET indicator.

2a. For the tax rate: Press [ TAX+ ], enter the tax rate, then press the [ % ]/

2b. For the currency rate: Press [ C2/EX RATE ]. Symbols such as $, €, £, A, B appear on the top left hand display as such: £ → $. Cycle through the symbols by pressing the [ + ] (↓RATES) key. Type in the rate and press [ % ]. You can view the rates going both ways by pressing the [ - ] key in this mode.

3. Press [ AC ] to return to normal calculator mode.

Example: $1 is converted to € 0.9027

Hold [ AC ] and [ % ] until SET appears. Press [ C2 ]. Press [ + ] until $ → € appears.

Enter 0.9027 and press [ AC ]. In this setting $ belongs to C1 and € belongs to C2.

$15 converted to Euros: 15 [ C2 ]. Display:

$ 15

RATE > 0.9027

€ 13.54

€200 to U.S. Dollars: 200 [ C1 ]. Display:

€ 200

RATE > 1.10778774786

$ 221.56

The three line display in used in a similar structure with tax calculations.

Change Calculation

The [ CHANGE CAL ] is used for change calculations, after a calculation is completed with the equals key [ = ]. I discovered this function by accident because the manuals I could find online did not give a thorough description of the function.

< calculation > [ = ] amount [ CHANGE CAL ]

Example 1:

Three items are priced 13.84, 17.01, and 19.99 are purchased. Assume that sales taxes are included in the price. You gave the cashier 100.

[ AC ] 13.84 [ + ] 17.01 [ + ] 19.99 [ = ]

Display:

GT = 50.84

100 [ CHANGE CAL ]

Display:

PRICE> 50.84

PAYMENT> 100.00

GT = 49.16

(Change: 49.16)

Example 2:

Three items are priced 11.95, 9.95, and 31.85. Sales tax is 9%. You give the cashier 100.

Press [ AC ] and [ % ] until SET appears. [ TAX + ] 9 [ % ]

[ AC ] 11.95 [ + ] 9.95 [ + ] 31. 85 [ = ]

Display:

GT 53.75

[ TAX+ ]

Display:

TAX 4.84

9%

T + GT 58.59

[ = ]

Display:

GT 58.59

100 [ CHANGE CAL ]

Display:

PRICE> 58.59

PAYMENT> 100.00

GT = 41.41

(Change: 41.41)

That is the Casio DF-320 TM in a nutshell. I understand that several calculators with the change calculation are or were sold in Asia, if memory serves me correctly.

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.