Descriptive STATISTICS: Standard Deviation

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 [navyfalcon1 (at) gmail.com]
 
Instructions: Click on the Related Article (in blue) to go to that Article
    Related Articles:-   StdDevSS    StDevFrm


 Formula          
       Mean      Standard Deviation      Variance  

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:
  STDEVFRQ (Standard Deviation Frequency) takes as input either a list (list) of values or summary statistics (data) values, (n = sample size, Σx = sum of items, Σx² = sum items sq) 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 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 7, do not use a line break [ENTER] 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.
    Program Memory = 406
 
        Outline: Standard Deviation w/Freq List
Outline:
Instructions: Click on the instruction (in blue) to go to that portion of the program
  Line 1. Clear
  Line 2 - 7. Instructions
  Line 12 - 15. Lbl D - input data
  Line 17 - 20. Lbl L - input list
  Line 21 - 23. freq list
  Line 24. n
  Line 25. Σx
  Line 26. Σx²
  Line 28. formula for mean
  Line 29. formula for variance
  Line 30. formula for standard deviation
  Line 32 - 44. Lbl X - display
  Line 38. fix 4
  Line 46. clear fix 4 (line 38)
    Examples
    Screenshots
    Reference
    Reference Links
 

prgm "STANDARD DEVIATION w/FREQ LIST"

Line  Commands or Statements  Comments
   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, Σx, Σx²"        |
   7.  ,"FOR DATA" End Instructions
   8.  Pause  
   9.  ClrHome  
 10.  Float  
 11.  Menu("STD DEV","LIST",L,"DATA",D  
 12.  Lbl D  Data Input
 13.  Input "n =",N  n = sample size
 14.  Input "Σx =",B  Σx = sumX
 15.  Input "Σx² =",Y  Σx² = sumXsquared
 16.  Goto X  
 17.  Lbl L  
 18.  Disp "DATA LIST  Input Data
 19.  Input "L1=",Str1  Input List L1
 20.  expr("{"+Str1->L1  
 21.  Disp "FREQ LIST  Input Freq
 22.  Input "L2=",Str2  Input List L2
 23.  expr("{"+Str2->L2  
 24.  sum(L2->N  n
 25.  sum(L1L2->B  Σx
 26.  sum(L1²L2->Y  Σx²
 27.  Lbl X  formula calculations & display
 28.  B/N ->C  calculates mean    x
 29.  ((Y - ((B) ²/N))/(N - 1)) ->V  calculates variance
 30.  √(V) -> S  standard deviation
 31.  ClrHome  Clear Screen & Display
 32.  Disp "n =  
 33.  Output(1,4,N  display n
 34.  Disp "Σx =  
 35.  Output(2,5,B  display Σx
 36.  Disp "Σx ² =  
 37.  Output(3,6,Y  display Σx ²
 38.  Fix 4  set decimal to 4 places
 39.  Disp "x =  
 40.  Output(4,4,C  display mean (x)
 41.  Disp "S² =  
 42.  Output(5,5,V  display variance (S ²)
 43.  Disp "S =  
 44.  Output(6,4,S  display standard deviation (S)
 45.  Pause  
 46.  Float  clear fix 4 (line 38)
 47.  ClrHome  
 
  Example
Data List: 14, 13, 12, 11, 10, 9, 8, 7, 6, 5
Freq List: 1, 2, 3, 3, 5, 3, 2, 1, 2, 1
Data: n = 23,  Σx = 226,  Σx² = 2,346 
Answers: n = 23,  Σx = 226,  Σx² = 2,346,  x = 9.8261  S² = 5.6957,  S = 2.3866



Screenshots:
TI-83 screenTI-83 screenTI-83 screenTI-83 screen
instructionsdata listanswers
 
Reference:
Instructions: Click on the command name (in blue) to go to information on that command
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
  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:
Instructions: Click on the link (in blue) to go to that link
  Information or Links:
TI-83 Basic Tutorial
This guide is here to help you understand how to program your TI 83, and more.
http://tatay.kenosha.wi.us/TiBasic/
 
Programming in TI Basic
Chapter 1: The Basics, Chapter 2: Creating Menus, Chapter 3: Graphics, Chapter 4: Misc.
http://www.arasian.com/vortex/83pbas/index.htm
 
TI-83 BASIC Guru Online
There is a definition of all the commands that are used in all of the tutorials in the Index.
Top of page, in blue outlined box (above Tutorial Contents) click on index.
http://bgo.netfirms.com/tutorials/index.html
 
TI Basic Developer
http://tibasicdev.wikidot.com/home
Welcome to the TI-83 section of TI-Basic Developer (TI|BD)! This section of the site covers how to make TI-Basic programs for the TI-83, TI-83+, TI-83+ Silver Edition (SE), TI-84+, and TI-84+ Silver Edition calculators
 
United TI Forums - TI Basic
TI-Basic - Use this forum to post questions and discuss the TI-BASIC programming language.
http://www.unitedti.org/forum/index.php?showforum=4 http://www.unitedti.org/forum/
 
FREE TUTORIALS © copyright 2000-2009 @ Cadet Career Counseling all rights reserved
Contact Webmaster at:(navyfalcon) e-mail