Showing posts with label deviation. Show all posts
Showing posts with label deviation. Show all posts

Saturday, August 27, 2022

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. 



Sunday, August 22, 2021

Numworks: Statistics and Regression Tutorial

Numworks:  Statistics and Regression Tutorial


Introduction


Numworks has two modes for statistical calculations and plotting:  Statistics and Regression.   Each of the two modes can hold up to three sets of data, each having their own separate graph color (red for the 1st, blue for the 2nd, green for the 3rd).  


Each mode has its own separate data, stored independently.   As far as I know so far, none of the data points or results can be accessed in any other mode.


Navigation of the modes are controlled by the keypad.  To change screens, keep press the up key until the header is selected.  


Statistics


The Statistics mode deals with univariate data (one-variable).   Two plots are offered:


*  Histogram Plots.  The bin width and starting point can be changed by pressing [ OK ] to bring up the options dialogue box.  


*  Box Plots.  Data for each lists calculated are:  minimum, 1st quarter, median, 3rd quarter, maximum



Regression


The Regression mode deals with bivariate data (two-variable).  The data and it's scatterplot are automatically displayed on the Graph screen.  The Data screen shows the mean, variance, and sums, along with regression model.


To change the regression, go to the Graph screen, scroll down to the regression model:


Linear:  ax + b

Proportional:  ax

Quadratic:  ax^2+bx+c

Cubic:  ax^3+bx^2+cx+d

Quartic:  ax^4+bx^3+cx^2+dx+e

Logarithmic: a*ln x+b

Exponential:  a*e^(bx)

Power: a*x^b

Trigonometric:  a*sin(bx+c)+d

Logistic:  c/(1+a*e^(-bx))


This menu will also to predict x and y values.



I hope you find this helpful, and highlight some of the other features of Numworks (other than Python).


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. 


Sunday, April 25, 2021

HP 12C: Statistical Signal to Noise Ratio

HP 12C:   Statistical Signal to Noise Ratio


Introduction and The Formula


There are many parameters that can be used to measure signal to noise ratio.   Today's formula will concentrate on the statistical measurements of univariate (1-variable) data.  The signal to noise ratio (SNR) is defined as the inverse of the ratio of the coefficient of variation, or the ratio of the mean to deviation.


SNR = mean / deviation


In the sources listed below (see the Sources section), they define the ratio as:


SNR = mean / standard deviation


However, the sources define standard deviation as:


√( ∑(x_i - mean for i = 1 to n) / (1 - n )


This is the formula for sample standard deviation, and that is the deviation this program will use.


HP 12C Program:  SNR


STEP KEY     KEY CODE

01 x-bar 43, 0

02 STO 0 44, 0

03 s         43, 48

04 RCL 0 45, 0

05 x<>y 34

06 ÷         10

07 GTO 00         43, 33, 00


Notes:


1.  x-bar displays the mean for both x and y data in their respective stacks.  Since we are only interested in the x data, I had to store the mean in R0.

2.  Similarly, calling up the s function displays the standard deviation for both x and y. 

3.  In statistics, only certain registers are available for storing values.  The HP 12C stores the following calculations during statistics:  R1: n,  R2: ∑x, R3: ∑x^2, R4: ∑y, R5: ∑y^2, R6: ∑xy.  


Instructions


1.  Clear the statistical data registers by pressing [ f ], [ SST ].

2.  Enter the data by using [ ∑+ ].

3.  Run the program by pressing [ R/S ].


Examples


Note:  The HP 12C is set to Fix 4 mode for these examples.  


Example 1: 

Data:  10, 35, 76, 49, 52, 56

SNR:  2.0883

(Mean:  46.3333,  Sample Standard Deviation:  22.1871)


Example 2:

Data:  50, 30, 20, 35, 25

SNR:  2.78000

(Mean:  32.0000,  Sample Standard Deviation: 11.5109)


Sources


BYJU'S  "Signal to Noise Ratio Formula"  BYJU'S Classes. 2021. https://byjus.com/signal-to-noise-ratio-formula/  Last Retrieved March 23, 2021  


EasyCalculation.com  "How to Calculate Signal to Noise Ratio (SNR) - Tutorial" https://www.easycalculation.com/statistics/learn-signal-to-noise-ratio.php Last Retrieved March 23, 2021


Wikipedia  "Signal-to-noise" https://en.wikipedia.org/wiki/Signal-to-noise_ratio  Retrieved February 27, 2021


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. 


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