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)]

 Formula  mean  Stan Dev  Var    
       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.
  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, Σx = sum items sq) and calculates the values (x = mean, S = 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
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. Σx
  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)
    Reference Links


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, Σx"       |
   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 "Σx =",Y Σx = 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(L1L2->Y Σx
 27. Lbl X formula calculations & display
 28. B/N ->C calculates mean    x
 29. ((Y - ((B) /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 = 
 37. Output(3,6,Y display Σx
 38. Fix 4 set decimal to 4 places
 39. Disp "x = 
 40. Output(4,4,C display mean (x)
 41. Disp "S = 
 42. Output(5,5,V display variance (S )
 43. Disp "S = 
 44. Output(6,4,S display standard deviation (S)
 45. Pause 
 46. Float clear fix 4 (line 38)
 47. ClrHome 
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,  Σx = 2,346 
Answers: n = 23,  Σx = 226,  Σx = 2,346,  x = 9.8261  S = 5.6957,  S = 2.3866

TI-83 screen TI-83 screen TI-83 screen TI-83 screen
instructions data list answers

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

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.
Programming in TI Basic
Chapter 1: The Basics, Chapter 2: Creating Menus, Chapter 3: Graphics, Chapter 4: Misc.
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.
TI Basic Developer
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
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counter on iweb Standard Deviation Tutorial Standard Deviation Definition: Standard deviation is a statistical measure of spread or variability.The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean. Standard Deviation - Calculator Online Calculation on STATISTICS Online Statistics Calculator, basic math statistics, Tutorial Free Statistics Calculators Free Calculators Free Statistics eBooks Free Download Statistics PDF eBook Statistics Homework Helpers Statistics and Probability Help is here Free Help for Statistics Homework or Projects Free Math and Statistics Homework Help Statistics Homework Help TutorTeddy offers free Statistics help and Probability help Free math lessons and math homework help Statistics Homework Help, Homework Helper Solves YOUR algebra homework problems with step-by-step help Statistics Forums Get free statistics help at the Statistics Forums Statistics and econometrics help forum Statistics is a field of mathematics that pertains to data analysis. Statistical methods and equations can be applied to a data set in order to analyze and interpret results, explain variations in the data, or predict future data. The standard deviation measures how much each reading differs from the mean (mathematic average) of all of the readings.