Descriptive STATISTICS: "Sum of Squares"

Introduction:  The deviations of scores about the mean of a distribution is the basis for most of the statistical tests we will learn. Since we are measuring how much a set of scores is dispersed about the mean we are measuring variability. We can calculate the deviations about the mean and express it as variance or standard deviation. Program by navyfalcon
 Formula      
     Variance          Standard Deviation  
NOTE: Using the TI-83 Calculator Emulator (which performs exactly like the TI-83 Calculator) and can be downloaded from TI-83 Calculator Emulator and following the calculator instructions (Using Your TI-83/84 calculator in Math) you can solve problems in arithmetic, algebra, geometry, trigonometry, statistics, and calculus.
Description:
  STDDEVSS (Standard Deviation "Sum of Squares") takes as input either a list (list) of values or summary statistics (data) values, (n = sample size, Sx = sum of items, S(x-x)² = sum of squares) and calculates the values (x = mean, S² = variance, and S = Standard Deviation [Std Dev]).
  Note: This program is in TI-BASIC and can be entered into the calculator by the calculator keyboard. Do not enter the outline, line numbers or comments, they are for reference only. The example programs below are for testing the program. If you get the values listed, the program was entered correctly. If not, check the listing and correct it. The program has been checked and tested.
  Note: -> is the [STO->] on the calculator keyboard.
  Note: for instructions line 2 through 8, do not use a line break or space between " and , but allow the code to wrap to the next line. Do not use more then 7 lines without a pause commant to display the text.
  Note: This program uses formulas in the program to calculate: mean, variance, standard deviation.
    Program Memory = 409

        Outline: SUM of SQUARES
Line 1. Clear
Line 2 - 9. Instructions
Line 14 - 17. Lbl D - input data
Line 19 - 22. Lbl L - input list
Line 32. formula for mean
Line 33. formula for variance
Line 34. formula for standard deviation
Line 36 - 49. Lbl X - display
Line 40. fix 4
Line 51. clear fix 4 (line 40)
    Examples
    Screenshots
    Reference
    Reference Links
    Online descriptive statistics calculator
    Statistics and Probability Tutorials
 

prgm "Sum of Squares"

   1.  ClrHome  Clear Screen
   2. Disp "SELECT LIST OR" Instructions
   3. ,"DATA TO BEGIN -"       |
   4. ,"USE COMMAS BTWN"       |
   5. ,"NUMBERS IN LIST"       |
   6.  ,"ENTER n, Sx,"        |
   7.  ,S(x-x)² FOR"        |
   8.  ,"DATA"  End Instructions
 10.  Pause  
 11.  ClrHome  
 12.  Float  
 13.  Menu("STD DEV","LIST",L,"DATA",D  Data Input
 14. Lbl D  
 15.  Input "n =",N  n = sample size
 16.  Input "Sx =",B  Sx = sumX
 17.  Input "S(x-x)² =",D  S(x-x)² sum of squares
 18.  Goto X  
 19. Lbl L  
 20.  Disp "DATA LIST  List Data
 21.  Input "L1=",Str1  
 22.  expr("{"+Str1->L1  
 23.  ClrHome 
 24. dim(L1->N n      No. items in L1
 25. sum(L1->B Sx    sum of no.s L1
 26. 0->D 
 27. L1->L2 
 28. B/N->C  calculates mean    x
 29. "L2-C"->L3 S(x-x)
 30. sum(L3²->D S(x-x
 31.  Lbl X  
 32. B/N->C  calculates mean    x
 33. D/(N - 1)->V  calculates variance
 34. √(V) -> S  standard deviation
 35.  ClrHome  
 36. Disp "n =  display n
 37.  Output(1,3,N  
 38.  Disp "Sx =  display Sx
 39.  Output(2,4,B  
 40. Fix 4  
 41.  Disp "x =  display x
 42.  Output(3,3,C  
 43.  Disp "Sx  display Sx
 44.  Output(4,2,"(x-x)²=  display sum of squares S(x-x
 45.  Output(4,9,D  
 46.  Disp "S² =  display variance (S²)
 47.  Output(5,4,V  
 48.  Disp "S=  display standard deviation (S)
 49.  Output(6,3,S  
 50.  Pause  
 51. Float  clear fix 4 (line 40)
 52.  ClrHome  
  Example:
Data List: 25, 24, 23, 22, 20, 18, 17, 16, 14, 10, 8
Data: n = 11,  Sx = 197, x = 17.9091,  S(x-x)² = 314.9091 
Answers: n = 11,  Sx = 197,  x = 17.9091  S² = 31.4909,  S = 5.6117
 
 
 
Screenshots:
TI-83 screenTI-83 screenTI-83 screenTI-83 screen
instructionsdata listanswers

Reference:
Commands or Statements:
  ClrHome   clears home screen
  dim(   returns the dimension (number of elements) of list
  Disp   displays text or value specified
  expr(   converts string to an expression
  Fix   sets fixed-decimal mode for number of decimal places
  Float   sets floating decimal mode. Displays decimal with no trailing zeros
  Goto   goes to label specified. Goto requires a line label be implemented as a destination
  Input   prompts for value to store to variable. Requires user input through keypad
  Lbl   creates a label of one or two characters
  Menu   generates a menu of up to seven items
  output( row, column)   displays text or value beginning at specified row and column
  Pause [value] Displays value; suspends program execution until you press [ENTER]. Pause with value displays value on the current home screen. Value can be scrolled
  round( value [,# decimals])  returns a number rounded to # decimals (=<9)
  Str# (# is number)   String: A sequence of characters is called a string
  sum(   returns the sum of elements in list
 
Reference:
Information or Links:
  Statistical Inference on the TI-83
This site contains typical problems and solutions on the general statistics topics of probability distributions, confidence intervals, hypothesis testing, analysis of variance, and correlation analysis.
http://www.wku.edu/~david.neal/statistics/
  Statistics on the TI-83
Descriptive Ststistics - Two variable Statistics - Probability Distribution - Inferential Statistics - Confidence Interval - Hypothrsis Testing - Chi-Square
http://www.cbu.edu/~wschrein/media/Stat/TI83Pman.pdf
  Calculator tutorials by Topic
Working with Univariate Data - Working With Bivariate Data - Probabilities - Confidence Intervals
http://calculator.maconstate.edu/calc_topics.html
  ticalc.org
TI-83/84 Plus Basic Math Programs (Statistics)
Basic Math Programs - Statistics
  United TI Forums - TI Basic
TI-Basic - Use this forum to post questions and discuss the TI-BASIC programming language.
http://www.unitedti.org/index.php?showforum=4
  
Online Calculator
  Online descriptive statistics calculator
http://25yearsofprogramming.com/javascript/descriptivestatistics.htm
This interactive calculator allows you to compute basic statistics on a set of numbers
  
Statistics Tutorials
  Statistics and Probability Tutorial
http://stattrek.com/lesson1/statistics-intro.aspx
Stat Trek's free, on-line Statistics and Probability tutorial
Descriptive Statistics - a good explanation
Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures
How to calculate simple statistics - "sum of squares"
In statistics, the most important calculations are the mean, mode, median, variance, and standard deviation (std dev)

Reference:
Statistics eBooks
Free Statistics eBooks
   This section contains free e-books and guides on Statistics
Introductory Statistics: Concepts, Models, and Applications
   The book, Introductory Statistics: Concepts, Models, and Applications, presented in the following pages represents over twenty years of experience in teaching the material contained therein.
Engineering Statistics Handbook
   Thr goal of this handbook is to help scientists and engineers incorporate statistical methods in their work.
Concepts & Applications of Inferential Statistics
   A free, full-length, and occasionally interactive statistics textbook.
Multivariate Statistics: Concepts, Models, and Applications
   An introductory statistics text for the social sciences
HyperStat Online Statistics Textbook
   An introductory-level textbook in statistics covering descriptive and inferential statistics.
Statistics: Methods and Applications
   A comprehensive textbook on statistics written for both novices and advanced analysts.

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