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  Std 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.
  STDEVFRM (Standard Deviation Formula) 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 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 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 = 386
        Outline: Standard Deviation w/Formula
Instructions: Click on the instruction (in blue) to go to that portion of the program
  Line 1. Clear
  Line 2 - 7. Instructions
  Line 12 - 16. Lbl D - input data
  Line 18 - 21. Lbl L - input list
  Line 23 - 26. calculator built-in formula [dim( and sum( ]. L1 squares X.
  Line 27. formula for mean
  Line 28. formula for variance
  Line 29. formula for standard deviation
  Line 31 - 43. Lbl X - display
  Line 37. fix 4
  Line 45. clear fix 4 (line 37)
    Reference Links


Line  Command or Statement  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  Input Data
 13.  Disp "DATA Input"  
 14.  Input "n =",N  n = sample size
 15.  Input "Σx =",B  Σx = sumX
 16.  Input "Σx =",Y  Σx = sumXsquared
 17.  Goto X  
 18.  Lbl L  Input List
 19.  Disp "LIST Input"  
 20.  Input "L1=",Str1  
 21.  expr("{"+Str1->L1  
 22.  ClrHome  clear screen - calculations
 23.  dim(L1->N  n       dim( calculator formula
 24.  sum(L1->B  Σx;    sum( calculator formula
 25.  sum(L1->Y  Σx    sum( calculator formula
 26.  Lbl X  formula calculations & display
 27.  B/N ->C  calculates mean    x
 28.  ((Y - ((B) /N))/(N - 1)) ->V  calculates variance
 29.  √(V) -> S  standard deviation
 30.  ClrHome  Clear screen - display
 31.  Disp "n =  
 32.  Output(1,4,N  display n
 33.  Disp "Σx =  
 34.  Output(2,5,B  display Σx
 35.  Disp "Σx =  
 36.  Output(3,6,Y  display Σx
 37.  Fix 4  set decimal to 4 places
 38.  Disp "x =  
 39.  Output(4,4,C  display mean (x)
 40.  Disp "S =  
 41.  Output(5,5,V  display variance (S)
 42.  Disp "S =  
 43.  Output(6,4,S  display standard deviation (S)
 44.  Pause  
 45.  Float  clear fix 4 (line 37)
 46.  ClrHome  
  Example 1:
List: 25, 24, 23, 22, 20, 18, 17, 16, 14, 10, 8
Data: n = 11,  Σx = 197,  Σx = 3843 
Answers: n = 11,  Σx = 197,  Σx = 3843,  x = 17.9091,  S = 31.4909,  S = 5.6117
  Example 2:
List: 13, 12, 11, 11, 10, 9, 9, 9, 6, 4
Data: n = 10,  Σx = 94,  Σx = 950 
Answers: n = 10,  Σx = 94,  Σx = 950,  x = 9.4000,  S = 7.3778,  S = 2.7162

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Texas Instruments TI-83 Plus Graphing Calculator; 64 H x 96mm W Screen


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
    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

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