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.

RPN with HP 15C & DM32: Min, Max, Midrange, Log Mean

RPN with HP 15C & DM32: Min, Max, Midrange, Log Mean

Introduction

These set of programs calculates four statistics:

(1) Minimum

(2) Maximum

(3) Midrange = (minimum + maximum) / 2

(4) Log Mean, using the maximum and minimum points. The general formula is:

log mean(T1, T2) = (T2 – T1) / ln(T2 / T1)

The program also enters data points into the statistics registers, allowing for one-variable statistics to be performed.

DM 32 Code

Initialization: LBL I

I01 LBL I

I02 STO M

I03 STO N

I04 CLΣ

I05 Σ+

I06 RTN

Enter data, maximum on the Y stack, minimum on the X stack: LBL T

T01 LBL T

T02 STO J

T03 Σ+

T04 RCL M

T05 RCL J

T06 x<y?

T07 STO M

T08 RCL N

T09 RCL J

T10 x>y?

T11 STO N

T12 RCL N

T13 RCL M

T14 STOP

T15 GTO T

Midrange: LBL M

M01 LBL M

M02 RCL N

M03 RCL+ M

M04 2

M05 ÷

M06 RTN

Log-Mean – Use maximum and minimum to determine the log-mean: LBL L

L01 LBL L

L02 RCL N

L03 RCL- M

L04 RCL N

L05 RCL÷ M

L06 LN

L07 ÷

L08 RTN

Variables Used:

J: temporary value

M = minimum

N = maximum

Instructions:

Step 1: Enter the first point and start the process by executing label I.

Step 2: Enter subsequent points and execute label T. The minimum is shown on the X stack, and the maximum is shown on the Y stack.

Step 3: To calculate the midrange, execute label M. To calculate the log mean, execute label L.

HP 15C Code

Initialization: LBL A

001	42, 21, 11	LBL A
002	44, 0	STO 0
003	44, 8	STO 8
004	44, 9	STO 9
005	44, 32	CLΣ
006	45, 0	RCL 0
007	49	Σ+
008	43, 32	RTN

Enter data, maximum on the Y stack, minimum on the X stack: LBL B

009	42, 21, 12	LBL B
010	44, 0	STO 0
011	49	Σ+
012	45, 8	RCL 8
013	45, 0	RCL 0
014	43, 30, 8	TEST 8, x<y?
015	44, 8	STO 8
016	45, 9	RCL 9
017	45, 0	RCL 0
018	43, 30, 7	TEST 7, x>y?
019	44, 9	STO 9
020	45, 9	RCL 9
021	45, 8	RCL 8
022	31	R/S
023	22, 12	GTO B

Midrange: LBL C

024	42, 21, 13	LBL C
025	45, 8	RCL 8
026	45, 40, 9	RCL + 9
027	2	2
028	10	÷
029	43, 32	RTN

Log-Mean – Use maximum and minimum to determine the log-mean: LBL D

030	42, 21, 14	LBL D
031	45, 9	RCL 9
032	45, 30, 8	RCL - 8
033	45, 9	RCL 9
034	45, 10, 8	RCL ÷ 8
035	43, 12	LN
036	10	÷
037	43, 32	RTN

Variables Used:

R0: temporary value

R8 = minimum

R9 = maximum

Statistical variables used (as default):

R2 = n

R3 = Σx

R4 = Σx^2

R5 = Σy

R6 = Σy^2

R7 = Σxy

Instructions:

Step 1: Enter the first point and start the process by executing label A.

Step 2: Enter subsequent points and execute label B. The minimum is shown on the X stack, and the maximum is shown on the Y stack.

Step 3: To calculate the midrange, execute label C. To calculate the log mean, execute label D.

Examples

Example 1:

0.2322	0.8252
0.8005	0.9262

Maximum: 0.9262

Minimum: 0.2322

Midrange: 0.5792

Log Mean: 0.5016

Example 2:

96	54	29
64	48	27

Maximum: 96

Minimum: 27

Midrange: 61.5

Log Mean: 54.3945

Sources

Volk, William. Engineering Statistics With A Programmable Calculator. McGraw-Hill Book Company: New York. 1982. pp. 8-9. ISBN 0-07-067552-X.

“Logarithmic Mean” Wikipedia. Last updated September 30, 2024. https://en.wikipedia.org/wiki/Logarithmic_mean. Last retrieved October 10, 2024.

Until next time,

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: The Spreadsheet

Casio fx-991CW: The Spreadsheet

Welcome to the Casio fx-991CW segment, which is planned to be every last Saturday of the month for 2025!

Spreadsheet

Screenshots are used the classpad.net website which contains the fx-991CW emulator.

The Casio fx-991CW has a Spreadsheet mode. The spreadsheet is 45 rows and 5 columns. The spreadsheet has a memory capacity of 2,380 bytes. The spreadsheet has basic spreadsheet functions. Data is saved as long as the calculator is in the Spreadsheet mode. Individual results can be stored in the calculator’s memory registers A, B, C, D, E, F, x, y, and z.

The spreadsheet of the fx-991CW can only contain numerical data. There are no labels.

Auto Calc is assumed to be on.

Sum, Mean, and Count of a Range of Cells

The sum of a range: = Sum( α# : β# )

The arithmetic mean of all the numbers in a range: = Mean( α# : β# )

The count of all cells that have a value stored: = Sum( α# : β# ) ÷ Mean( α# : β# )

The count has to be constructed because there is no count function in the fx-991CW. Since Sum is Σx and Mean is Σx / n. Hence count, or n, is: Count = Sum / Mean = Σx / (Σx / n) = Σx * (n / Σx) = n.

The Sum, Count, and the colon character ( : ) are found in the Catalog.

Example:

	A	B
1	45	88
2	25	76
3	93	39

Min, Max, and Statistical Range of a Range of Cells

The minimum value of a range of cells: = Min( α# : β# )

The maximum value of a range of cells: = Max( α# : β# )

The statistical range of a range of cells: = Max( α# : β# ) - Min( α# : β# )

Example:

	A	B
1	45	88
2	25	76
3	93	39

Multiply a Range of Cells with a Constant Rate

We can apply a formula to a range of cells through the Tools menu. The Fill Formula dialogue:

Fill Formula

Fill = (start the formula with the cell you are currently at)

Range : α# : β#

> Confirm

To make a cell absolute, attack a dollar sign, to both the column letter and row number. The dollar sign ( $ ) is in the Catalog.

Example:

	A	B
1		0.85
2	59.95
3	42.75
4	73.95

Storing a Cell’s Value

Exiting the Spreadsheet mode or turning the calculator off will erase the contents of the Spreadsheet. A way to store values permanently is to store the cell’s contents in one of the variables (A – F, x, y, z). To store a value:

1. Go to the cell.

2. Press the [ VARIABLE ] button.

3. Select a variable and press [ EXE ].

4. Select Store.

The value is now stored in the variable, which can be used in other modes. Unlike the spreadsheet, values stored in values are kept until a reset.

I hope you find this helpful.

Until next time,

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.