Statistics: "Sum of Squares"

The distance from any point in a collection of data, to the mean of the data, is the deviation. If all such deviations are squared, then summed, we have the "sum of squares" for that data.

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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)²
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)²
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

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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Formula
	Variance	Standard Deviation

Screenshots:

instructions	data	list	answers