Spotlight: Sharp EL-520L

 Spotlight: Sharp EL-520L

Quick Facts

Model: EL-520L

Company: Sharp

Type: Solar Scientific Algebraic

Power: Solar with battery backup, 2 x LR 44

Case: Slide case

Memory: 7 memory registers: A, B, C, D, X, Y, M (M has memory addition and subtraction)

Years in Production: 1998

Display: 2 line, with results up to 10 digits

Shout out to Spaceboy Jeffy’s Vintage Emporium from where I purchased the calculator.

Scientific Calculations in Two Lines

The Sharp EL-520L is an early two-line scientific calculator. The top line is where mathematical expressions are entered, where the bottom line is where the results are displayed.

Expressions are entered as written, as noted by Sharp’s ADVANCED D.A.L. (Direct Algebraic Logic.

Example (degrees mode, float mode):

(top | bottom)

0.5; Screen: DEG | 0.5

×; Screen: DEG 0.5*_ |

e^; Screen: DEG 0.5*e^_ |

(sin 10°); Screen: DEG 0.5*e^(sin10) |

=; Screen: DEG 0.5*e^(sin10)= | 0.594818475

Modes

The modes of the EL-520L are controlled by the MODE keys and two toggle keys:

Toggle keys:

[ DRG ]: Change mode through the degrees, radians, and grads cycle. This is how the angle mode is changed on scientific calculators from the 1980s.

[ 2ndF ] [ DRG ] ( DRG> ): A variation of angle change. In this variation, a conversion of angle measurement.

[ 2ndF ] [ . ] (FSE): This the display format toggle: Floating point (no indicator), fixed point (FIX), scientific notation (SCI), engineering notation (ENG). The TAB function, accessed by [ 2ndF ] [ +/- ], set the number of decimal points in the fixed point, scientific notation, and engineering notation format.

There is also a modify (MDF) function that internally rounds the result to the fixed decimal point settings. The modify function does not affect anything stored to variables, however. I wish there was a round function (Round(n, decimal points)) instead, to be honest.

The Mode Key:

The [ MODE ] key offers three modes:

0: Normal. Normal calculator mode.

1: STAT x: Single variable statistics. The [ STO ] key becomes the comma key and memory plus key [ M+ ] becomes the data entry key.

2: STAT xy: Linear regression mode. The data is fit to the equation y = a + bx where a is the y-intercept and b is the slope.

In the statistic modes, the variables (A -D, X, Y, M) are not operable.

Replay and Editing Keys

In Normal mode, there are three editing functions:

[ DEL ]: The standard delete character.

[ 2^nd ] [ ← ] (⟲): Takes the cursor to the beginning of the last expression

[ 2^nd ] [ → ] ( ? ): Takes the cursor to the next number after the cursor’s position

There is no insert/replace mode. It seems like Sharp was experimenting with editing commands.

Order of Operations (Quirks?)

In a lot of algebraic calculators, the square function has higher priority than negation. Entering -4² returns -16.

Implied multiplication gets a higher priority than division and regular multiplication. Therefore if we enter the infamous expression:

6÷2(1+2) returns 1 instead of 9.

This is known as PEJMDAS where J is juxtaposition, or implied multiplication. For more information, please see The How and Why of Mathematics’ video from 2019:

https://www.youtube.com/watch?v=4x-BcYCiKCk

I’ll leave the debate at this point. Of course, when it doubt, use extra parenthesis or insert an additional multiplication sign ( × ).

One quirk: To insert variables (A, B, C, D, X, Y, M) into expressions, press [ 2ndF ] [ RCL ] (ALPHA).

Final Thoughts

The Sharp EL-520L is nice, basic level calculator with the ability to enter expressions. The EL-520L has a nice amount of the features that will satisfy most needs.

Source

Flow Simulation, Ltd. “Sharp EL-520 (ADVANCED D.A.L.)” calculator.org https://www.calculator.org/calculators/Sharp_EL-520L.html

Eddie

All original content copyright, © 2011-2026. 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.

Numworks (Python): Control Charts

 Numworks (Python): Control Charts

The following Python script develops the x-bar and R control charts.

Formulas used:

mean_average = Σ(mean of each sample)

range_average = Σ(range of each sample)

x-Bar Chart:

low = mean_average - a2 * range_average

high = mean_average + a2 * range_average

R chart:

low = d3 * range_average

high = d4 * range_average

Python script (done with Numworks): ctrlchart.py

from math import *

# control chart function

# run as a defined function

# HP 65 Stat Pac 2, 1975

def ctrlchart():

  #elements

  a2=[0,0,1.88,1.02,.73,.58,.48,.42,.37,.34,.31,.29,.27,.25,.24,.22,.21,.20,.19,.19,.18]

  d3=[0,0,0,0,0,0,0,.08,.14,.18,.22,.26,.28,.31,.33,.35,.36,.38,.39,.4,.41]

  d4=[0,0,3.27,2.57,2.28,2.11,2,1.92,1.86,1.82,1.78,1.74,1.72,1.69,1.67,1.65,1.64,1.62,1.61,1.6,1.59]

  # calculation

  meansum=0

  rangesum=0

  n=int(input("number of samples? "))

  m=int(input("sample size (2-20)? "))

  for i in range(n):

    x=[]

    for j in range(m):

      # adjust to show proper numbering

      s="x("+str(i+1)+","+str(j+1)+")? "

      p=eval(input(s))

      x.append(p)

    rangesum+=max(x)-min(x)

    meansum+=sum(x)/m

  rangeavg=rangesum/n

  meanavg=meansum/n

  lowmean=meanavg-rangeavg*a2[m]

  highmean=meanavg+rangeavg*a2[m]

  lowrange=d3[m]*rangeavg

  highrange=d4[m]*rangeavg

  print("x-bar chart")

  print("L: "+str(lowmean))

  print("H: "+str(highmean))

  print("range chart")

  print("L: "+str(lowrange))

  print("H: "+str(highrange))

Example 1:

5 samples (n = 5)

Sample size: 4  (m = 4)

Sample 1:  4.3, 4.2, 4.3, 5.0

Sample 2:  4.1, 4.1, 4.6, 3.6

Sample 3:  4.0, 4.5, 4.3, 3.7

Sample 4:  3.9, 4.7, 4.4, 5.1

Sample 5:  4.2, 5.2, 4.9, 5.3

x-Bar chart:

Low:  3.7046

High:  5.1354

R chart:

Low:  0

High:  about 2.2345

Example 2:

2 samples (n = 2)

Sample Size: 7 (m = 7)

Sample 1:  48, 58, 53, 56, 57, 59, 55

Sample 2:  56, 46, 48, 49, 63, 52, 51

x-Bar chart:  

Low:  47.33428571428571

High:  59.09428571428571

R chart:

Low:  1.12

High: 26.88

Source

“x-bar and R Control Charts”. HP 65 Stat Pac 2. Hewlett Packard. 1975. pp. 98 – 101

Eddie

All original content copyright, © 2011-2026. 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-451 Calculator

Spotlight: Casio fx-451 Calculator

Quick Facts

Model: fx-451

Company: Casio

Type: Solar Scientific Algebraic

Memory: 1 (store, recall, exchange (X←→M), sum (M+), subtract (M-))

Years in Production: 1985 to 1987 per calculator.org (https://www.calculator.org/calculators/Casio_fx-451.html)

Display: 10 digits

Casio Ledudu’s page on the fx-451: https://casio.ledudu.com/pockets.asp?lg=eng&type=1016

Folding Calculator Power

The Casio fx-451 is a folding scientific calculator. On the left side, there are the arithmetic keys, the shift, mode, and on keys, the display (10 digits), and the solar panel that operates the calculator. The right side has touch, rubber-like, membrane keys. The right side has all the scientific, statistical, fraction, base conversion, and imperial/metric conversions.

You can see my review of the fx-450 from 2018 here: https://edspi31415.blogspot.com/2018/07/retro-review-casio-fx-450-calculator.html

The available modes for the fx-451 are:

. (decimal point): SD (Standard Deviation), single variable statistics. Statistics functions are marked in blue.

0: DEC. Decimal mode. This is also the calculator’s normal/computation mode.

1: BIN. Binary integer mode (base 2). Boolean logic operators are available and are marked in green.

2: OCT. Octal integer mode (base 8). Boolean logic operators are available and are marked in green.

3: HEX. Hexadecimal integer mode (base 16). Boolean logic operators and the letter digits A-F (A=10 to F=15), are available and are marked in green.

4: DEG. Degree angle mode.

5: RAD: Radians angle mode.

6: GRA: Gradians angle mode.

7: FIX: Fixed point decimal setting

8: SCI: Scientific notion decimal setting.

9: NORM: Floating point decimal setting. Numbers less than 0.01 are shown in scientific notation form.

The engineering keys, [ENG] and [←ENG], temporarily show the number in display using scientific notation where the exponents are in multiples of 3 (i.e. 10^-6, 10^-3, 10^0, 10^3, 10^6, etc.)

Like many Casio scientific calculators, the fx-451 sports the fraction key [a b/c], allowing both entry of fractions (proper and mixed), and conversions between fractions and decimal approximations.

In addition, the fx-451 has nine scientific constants. (by pressing [SHIFT] [1-9]).  The constants are:

1. Speed of Light (c)

2. Plank’s constant (h)

3. Universal gravitational constant (G)

4. Electron charge (e)

5. Mass of an electron (me)

6. Atomic mass constant (u)

7. Avogadro’s constant (Na)

8. Boltzmann constant (k)

9. Molar volume of ideal gas (Vm)

All units are in SI units, and are listed with the constant on the keyboard.

The fx-451 Adds Imperial/Metric Conversions

(fx-450 (top), fx-451 (bottom))

The fx-451 is a later version of the fx-450 and has added a set of eight imperial/metric conversions:

Temperature: degrees Fahrenheit/Celsius

Length: inches/millimeters

Volume: gallons/liters, ounces/grams

Mass: pounds/kilograms

Energy: calories/Joules

Pressure: inches of Mercury/kilopascals, atm/megapascals

Conversions are called by the two arrow keys [ ← ] and [ → ], and are they are marked in gold. I always find conversions to be a welcome addition to any calculator.

Solar Power

Like it’s cousin, the fx-450, the fx-451 operates only by solar and light power, hence no other batteries are required.

This is a fun calculator to have, and Casio does a really good job of including lots of features even in its basic scientific calculators.

Eddie

All original content copyright, © 2011-2026. 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.

BASIC vs. Python: Mean and Standard Deviation by an Iterative Method

BASIC vs. Python: Mean and Standard Deviation by an Iterative Method

Calculators Used:

BASIC: Sharp EL-5500 III

Python: Casio fx-CG 100

Introduction

The following code calculates the sum, mean, and standard deviation of a data set. The method that will be used is from voidware.com, which suggests an iterative method, as follows (Voidware):

M_0 = 0, S_0 = 0, n = 0

Loop with data point X:

M_n+1 = M_n + (X – M_n) ÷ (n + 1)

S_n+1 = S_n + (X – M_n) × (X – M_n+1)

n = n + 1

When all the data as been tabulated:

S = √(S ÷ (n – 1))

M: mean

S: standard deviation

Source

“Standard Deviation” Voidware. http://www.voidware.com/sd.htm Website was last updated in 2018. Last Retrieved July 4, 2025.

BASIC: Sharp EL-5500 III

10 PRINT "ONE VAR STATS"

12 CLEAR

30 INPUT "DATA? "; X

32 E=M+(X-M)*(N+1)

34 S=S+(X-M)*(X-E)

36 N=N+1

38 M=E

40 U=U+X

42 INPUT "MORE? (1=YES) "; C

44 IF C=1 THEN 30

60 S=√(S/(N-1))

70 PRINT "# DATA= "; N

72 PRINT "SUM= "; U

74 PRINT "MEAN= "; M

76 PRINT "STD DEV= "; S

78 END

Notes:

CLEAR: clears all the variables A-Z and resets their values to zero

PRINT: pauses the screen while the message is displayed

Python: Casio fx-CG 100

(Can be we used with any calculator with Python)

# one var stat without the math module

# voidware.com/sd.htm

def onevar(data):

  # set up

  m,s,u,n=0,0,0,0

  for i in data:

    e=m+(i-m)/(n+1)

    s+=(i-m)*(i-e)

    n+=1

    m=e

    u+=i

  s=(s/(n-1))**0.5

  return [n,u,m,s]

Notes:

We can store multiple values to variables at once. Example:

var4, var3, var2, var1 = value1, value2, value3, value4

Storage Arithmetic:

s+=expression -> s=s+expression

s-=expression -> s=s-expression

s*=expression -> s=s*expression

s/=expression -> s=s/expression

Example

Data set:

n = 1: x = 105

n = 2: x = 107

n = 3: x = 86

n = 4: x = 96

n = 5: x = 113

Data Structure: [105, 107, 86, 96, 113]

Results:

# DATA: 5 (N)

SUM: 507 (U)

MEAN: 101.4 (M)

STD DEV: 10.54988151 (S)

Eddie

All original content copyright, © 2011-2026. 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.

The author does not use AI engines and never will.

Quick Review: Casio fx-9910CW 2nd Edition

Quick Review: Casio fx-9910CW 2^nd Edition

The Casio fx-9910CW 2^nd Edition is an update of the fx-991CW first released in 2023.

Product Pages

United States:

https://www.casio.com/us/scientific-calculators/product.FX-9910CW/

The fx-9910CW has two keyboards: black with gold font and pink with purple font (limited). I have one each and Casio has improved on the readability on the pink edition with the dark purple font.

I’m sure this model will be available world wide soon.

What’s the Same and What’s Different

Overall, the fx-9910CW 2^nd Edition has the same mathematical features as the fx-991CW. The modes included are:

Calculate: the main app for mathematical calculations

Statistics: 1 and 2 variable with seven regression models:

Linear:  y=a+bx

Quadratic: y=a+bx+cx^2

Logarithmic:  y=a+b*ln(x)

Exponential:  y=a*e^(bx)

Power I:  y=a*b^x

Power II: y=a*x^b

Inverse:  y=a+b/x

Statistical graphs may be generated with the QR feature.

Distribution: Binomial, Normal, and Poisson distributions, along with their inverses. The functions work with lower-tail probabilities (-∞ or 0 to x).

Spreadsheet: 5 columns, 45 rows. 2,380 byte memory.

Table: Generate a table for up to two functions f(x) and g(x). Generate graphs with the QR feature.

Equations: Linear systems (up to 4 x 4), polynomials up to 4^th order, and a general equation solver.

Inequalities: Solve inequalities for polynomials up to the 4^th order.

Complex Numbers: Complex number arithmetic with polar/rectangular conversion, integer powers, real/imaginary parts, conjugate

Base N: Base mode for the traditional decimal, hexadecimal, octal, and binary basis. Binary integers are up to 31 bytes with one sign bit.

Matrix: Four matrices, up to size 4 x 4, with basic matrix functions such as determinant, transpose, and inverse.

Vector: Four vectors, 2D or 3D, with dot product, cross product, and norm.

Math Box: Dice Roll and Coin Toss simulations

47 scientific constants (SI units) and unit conversions

We still have the newer Casio style of navigation keys, the Home Key, the Back Key, the Settings key, and the Scroll up and down keys.

What is different?

First, the fx-9910CW is not solar powered, but instead runs on a single AAA battery.

Welcome changes:

The menus all have short cut keys! This eliminates the requirement to scroll down menus, which some get long, to find the sub menus and functions. This makes the operating the calculator a lot easier and more efficient, eliminating additional key strokes by repeatedly pressing the arrow keys.

For example, to get the absolute value in Calculate mode, press [ CATALOG ], [ 3 ] for Numeric Calc, [ 1 ] for Absolute Value.

In the same mode, we call up the Speed of Light constant (c), press [ CATALOG ] , [ 7 ] for Sci Constants, [ 1 ] for Universal, and [ 3 ] for c.

There is a setting to turn the hide the shortcut numbers but thankfully it won’t turn off the ability to navigate by using short cut keys.

The 10^[] and FORMAT keys return to familiar form! Like the fx-CG 100, we have an option on how the 10^[] and FORMAT keys operate.

10^[] Key:

(1) Power: Acts like a power key like the fx-991CW. I read that there are potential problems with calculating with this key leaving calculations to return unexpected answers.

(2) Sci. Notat: This returns this key to the traditional scientific notation key. When this option is selected, the 10^ is shown in a small font. This key now acts like the [ EE ] or [ EXP ] keys on other scientific calculators. This is the default setting.

FORMAT Key:

(1) -π√ ←→ Decimal. Pressing the FORMAT key just toggles between decimal and the exact (when available) format of answers. This brings back the beloved [ S←→D ] key. This is the default settings.

(2) Format Menu. This is the format menu that is presented, similar to the fx-991CW. We trade off the quick toggle for additional formatting options.

Shortcut Catalog. Pressing [ SHIFT ] [ CATALOG ] is a new feature and provides a listing of all mathematical functions available in the active mode. Up to 15 functions are shown, using the arithmetic keys (+, -, ×, ÷) and the decimal point (.) as additional shortcut keys. The shortcut catalog does not have the conversions or constants.

These changes are welcome and enhance the operating experience of the calculator.

My next wish is that the fx-9910CW included the Algo mode (algorithm mode) that allowed small programs (via a mix of Scratch and Casio Basic). You can find out more details here:

https://edspi31415.blogspot.com/2025/08/casio-fx-92-college-plotting-lines.html

I just think the algorithm mode is neat, gives students an introduction to programming, and would have fit the fx-9910CW well.

Great job, Casio. I think Casio listened to calculator users and brought back these improvements, and brought it more in line with operating the fx-CG 100/Graph Math Plus. If you were hesitant about the fx-991CW, the fx-9910CW 2^nd Edition is a good time to jump in.

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.

Casio fx-991CW: Arc of a Quadratic Curve

Casio fx-991CW: Arc of a Quadratic Curve

All screen shots will be taken with the https://www.classpad.app/ website.

Introduction

We are given three points: (x1, y1), (x2, y2), and (x3, y3) which are connected to a quadratic curve:

y(x) = a + b * x + c * x^2

with it’s derivative:

y’(x) = b + 2 * c * x

We assume that all three x-values are unique, therefore x1 ≠ x2, x2 ≠ x3, and x1 ≠ x3.

The arc length is the integral: ∫( √(1 + (b + 2 * c * x)^2 dx, min(x), max(x))

In curve fitting, if we only have three points, the quadratic curve will fit all three points.

Procedure

We can do the entire calculation in the Statistics app of the fx-991CW.

1. Go to the Statistics app by pressing [ Home ], selecting Statistics.

2. Enter the three points. If you need to, you can clear the lists by selecting Tools > Edit > Delete All.

3. Press [OK] (or [EXE] ), select Statistics Calc, y = a + b * x + c * x^2, and then press [OK] (or [EXE]) again. The Statistics Calc will allow us to make calculations using the statistics variables.

4. Calculate the integral:

∫ ( √(1 + (b + 2 * c * x)^2), min(x), max(x))

∫: Catalog > Func Analysis > Integration

b: Catalog > Statistics > Regression > b

c: Catalog > Statistics > Regression > c

min(x): Catalog > Statistics > Regression > Min/Max > min(x)

max(x): Catalog > Statistics > Regression > Min/Max > min(x)

Let’s walk through an example:

Points: (0,0), (5,4), (7,2)

Arc length: 9.97139451

You can see the procedure through the screen shots below:

Quadratic Curve:

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.

Numworks: Estimating the Speed of Sound in Water

 Numworks: Estimating the Speed of Sound in Water

Generally, the speed of sound in water is faster than the speed of sound in air. Is there an easy way to estimate the speed of sound in water using curve fitting? I will use the Numworks’ Regression App. The online simulator of Numworks: https://www.numworks.com/simulator/ .

* For readability, I consolidated some screen shots.

The data, from The Engineering Toolbox (see Source below) is shown in below:

SI Units

Temperature in °C	Speed of sound in m/s (meters/second)
0	1403
5	1427
10	1447
20	1481
30	1507
40	1526
50	1541
60	1552
70	1555
80	1555
90	1550
100	1543

https://www.engineeringtoolbox.com/sound-speed-water-d_598.html

Of the curve fits available, I found the best fits were to be with polynomial regression.

Quadratic Regression: y = a2 * x^2 + a1 * x + a0

y = -0.02736013 * x^2 + 4.059449 * x + 1407.3398

where y is the speed of sound in water (m/s) and x is the temperature (°C). The r^2 parameter is 0.9980768, which is pretty good given the raw data is only rounded the nearest integer. The Numworks also offers residual plot, which is the difference between predicted and given data. From the residual plot, the biggest difference was at x = 0.

Quartic Regression: y = a4 * x^4 + a3 * x^3 + a2 * x^2 + a1 * x + a0

If we are looking for better accuracy, we could use the quartic regression, where r^2 parameter is 0.99981. From the residual plot, the biggest difference was located at x = 60.

y = -7.955665 * 10^-7 * x^4 + 2.523644 * 10^-4 * x^3 – 0.05122094 * x^2 + 4.782147 * x + 1403.692

For a quick calculation, the quadratic equation could be sufficient enough.

Source

The Engineering ToolBox (2004). Water - Speed of Sound vs. Temperature. [online] Available at: https://www.engineeringtoolbox.com/sound-speed-water-d_598.html. Accessed May, 2025.

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.

The author does not use AI engines and never will.