Introductory Statistics
Mathematics and StatisticsAppendix G: Notes for the TI83, 83+, 84, 84+ Calculators
Quick Tips
Legend
represents yellow command or green letter behind a key[ ]
represents items on the screen< >
To adjust the contrastPress
To capitalize letters and wordsPress
To correct a mistakeIf you hit a wrong button, just hit
To write in scientific notationNumbers in scientific notation are expressed on the TI83, 83+, 84, and 84+ using E notation, such that...
 4.321 E 4 = $\text{4}\text{.321}\times {\text{10}}^{4}$
 4.321 E –4 = $\text{4}\text{.321}\times {\text{10}}^{\mathrm{\u20134}}$
To transfer programs or equations from one calculator to another:Both calculators: Insert your respective end of the link cable cable
and press
[LINK]
.
Calculator receiving information:
 Use the arrows to navigate to and select
<RECEIVE>
 Press
Calculator sending information:
 Press appropriate number or letter.
 Use up and down arrows to access the appropriate item.
 Press
 Press right arrow to navigate to and select
.<TRANSMIT>
 Press
Both calculators: Insert your respective end of the link cable cable
Both calculators: press
[QUIT]
to exit when done.Manipulating OneVariable Statistics
Data  Frequency 
–2  10 
–1  3 
0  4 
1  5 
3  8 
To begin:

Turn on the calculator.

Access statistics mode.

Select
to clear data from lists, if desired.<4:ClrList>
Enter list
to be cleared.[L1]
,[L1]
Display last instruction.
[ENTRY]
Continue clearing remaining lists in the same fashion, if desired.
,[L2]
Access statistics mode.
Select
<1:Edit . . .>
Enter data. Data values go into
. (You may need to arrow over to[L1]
).[L1]
Type in a data value and enter it. (For negative numbers, use the negate () key at the bottom of the keypad).
 Continue in the same manner until all data values are entered.
In
, enter the frequencies for each data value in[L2]
.[L1]
Type in a frequency and enter it. (If a data value appears only once, the frequency is "1").
 Continue in the same manner until all data values are entered.
Access statistics mode.
 Navigate to
.<CALC>
Access
.<1:1var Stats>
Indicate that the data is in
...[L1]
,[L1]
...and indicate that the frequencies are in
.[L2]
,[L2]
 The statistics should be displayed. You may arrow down to get remaining statistics. Repeat as necessary.
Drawing Histograms
We will construct two histograms with the builtin STATPLOT application. The first way will use the default ZOOM. The second way will involve customizing a new graph.

Access graphing mode.
[STAT PLOT]

Select
to access plotting  first graph.<1:plot 1>

Use the arrows navigate go to
to turn on Plot 1.<ON>
,<ON>

Use the arrows to go to the histogram picture and select the histogram.
 Use the arrows to navigate to
.<Xlist>

If "L1" is not selected, select it.
,[L1]
 Use the arrows to navigate to
.<Freq>

Assign the frequencies to
.[L2]
,[L2]
Go back to access other graphs.
[STAT PLOT]
 Use the arrows to turn off the remaining plots.
 Be sure to deselect or clear all equations before graphing.
To deselect equations:
Access the list of equations.
Select each equal sign (=).
 Continue, until all equations are deselected.
To clear equations:
Access the list of equations.
Use the arrow keys to navigate to the right of each equal sign (=) and clear them.
 Repeat until all equations are deleted.
To draw default histogram:
Access the ZOOM menu.
Select
.<9:ZoomStat>
 The histogram will show with a window automatically set.
To draw custom histogram:
 Access window mode to set the graph parameters.

 ${X}_{\mathrm{min}}=\mathrm{\u20132.5}$
 ${X}_{\mathrm{max}}=3.5$
 ${X}_{scl}=1$ (width of bars)
 ${Y}_{\mathrm{min}}=0$
 ${Y}_{\mathrm{max}}=10$
 ${Y}_{scl}=1$ (spacing of tick marks on yaxis)
 ${X}_{res}=1$
 Access graphing mode to see the histogram.
To draw box plots:
Access graphing mode.
[STAT PLOT]
Select
to access the first graph.<1:Plot 1>
Use the arrows to select
and turn on Plot 1.<ON>
Use the arrows to select the box plot picture and enable it.
 Use the arrows to navigate to
.<Xlist>
If "L1" is not selected, select it.
,[L1]
 Use the arrows to navigate to
.<Freq>
Indicate that the frequencies are in
.[L2]
,[L2]
Go back to access other graphs.
[STAT PLOT]
 Be sure to deselect or clear all equations before graphing using the method mentioned above.
View the box plot.
[STAT PLOT]
Linear Regression
Sample Data
The following data is real. The percent of declared ethnic minority students at De Anza College for selected years from 1970–1995 was:
Year  Student Ethnic Minority Percentage 
1970  14.13 
1973  12.27 
1976  14.08 
1979  18.16 
1982  27.64 
1983  28.72 
1986  31.86 
1989  33.14 
1992  45.37 
1995  53.1 
To enter data and do linear regression:
ON Turns calculator on.
 Before accessing this program, be sure to turn off all plots.
Access graphing mode.
[STAT PLOT]
Turn off all plots.
 Round to three decimal places. To do so:
Access the mode menu.
[STAT PLOT]

Navigate to
and then to the right to<Float>
.<3>

All numbers will be rounded to three decimal places until changed.

Enter statistics mode and clear lists
and[L1]
, as describe previously.[L2]

Enter editing mode to insert values for x and y.
 Enter each value. Press
To display the correlation coefficient:
Access the catalog.
[CATALOG]
Arrow down and select
<DiagnosticOn>
 $r$ and $r^{2}$ will be displayed during regression calculations.
Access linear regression.

Select the form of y = a + bx.
The display will show:
LinReg
 y = a + bx
 a = –3176.909
 b = 1.617
 r = 2 0.924
 r = 0.961
This means the Line of Best Fit (Least Squares Line) is:
 y = –3176.909 + 1.617x
 Percent = –3176.909 + 1.617 (year #)
To see the scatter plot:

Access graphing mode.
[STAT PLOT]

Select
To access plotting  first graph.<1:plot 1>

Navigate and select
to turn on Plot 1.<ON>
<ON>
 Navigate to the first picture.

Select the scatter plot.
 Navigate to
.<Xlist>

If
is not selected, press[L1]
to select it.[L1]

Confirm that the data values are in
.[L1]
<ON>
 Navigate to
.<Ylist>

Select that the frequencies are in
.[L2]
,[L2]

Go back to access other graphs.
[STAT PLOT]
 Use the arrows to turn off the remaining plots.
 Access window mode to set the graph parameters.
 ${X}_{\mathrm{min}}=1970$
 ${X}_{\mathrm{max}}=2000$
 ${X}_{scl}=10$ (spacing of tick marks on xaxis)
 ${Y}_{\mathrm{min}}=0.05$
 ${Y}_{\mathrm{max}}=60$
 ${Y}_{scl}=10$ (spacing of tick marks on yaxis)
 ${X}_{res}=1$
 Be sure to deselect or clear all equations before graphing, using the instructions above.
 Press the graph button to see the scatter plot.
To see the regression graph:

Access the equation menu. The regression equation will be put into Y1.

Access the vars menu and navigate to
.<5: Statistics>
 Navigate to
.<EQ>

contains the regression equation which will be entered in Y1.<1: RegEQ>
 Press the graphing mode button. The regression line will be superimposed over the scatter plot.
To see the residuals and use them to calculate the critical point for an outlier:

Access the list. RESID will be an item on the menu. Navigate to it.
,[LIST]
<RESID>

Confirm twice to view the list of residuals. Use the arrows to select them.
 The critical point for an outlier is:
$1.9V\frac{\mathrm{SSE}}{n2}$ where:
 $n$ = number of pairs of data
 $\mathrm{SSE}$ = sum of the squared errors
 $\sum \mathrm{residual}^{2}$

Store the residuals in
.[L3]
,[L3]

Calculate the $\frac{\mathrm{(residual)}^{2}}{n2}$. Note that $n2=8$
,[L3]

Store this value in
.[L4]
,[L4]

Calculate the critical value using the equation above.
,[V]
[LIST]
,[L4]
 Verify that the calculator displays: 7.642669563. This is the critical value.
 Compare the absolute value of each residual value in
to 7.64. If the absolute value is greater than 7.64, then the (x, y) corresponding point is an outlier. In this case, none of the points is an outlier.[L3]
To obtain estimates of y for various xvalues:There are various ways to determine estimates for "y." One way is to substitute values for "x" in the equation. Another way is to use the
TI83, 83+, 84, 84+ instructions for distributions and tests
Distributions
Access
DISTR
(for "Distributions").
For technical assistance, visit the Texas Instruments website at http://www.ti.com and enter your calculator model into the "search" box.
Binomial Distribution
corresponds to P(X = x)binompdf(n,p,x)
corresponds to P(X ≤ x)binomcdf(n,p,x)
 To see a list of all probabilities for x: 0, 1, . . . , n, leave off the "
" parameter.x
Poisson Distribution
corresponds to P(X = x)poissonpdf(λ,x)
corresponds to P(X ≤ x)poissoncdf(λ,x)
Continuous Distributions (general)
 $\infty $ uses the value –1EE99 for left bound
 $\infty $ uses the value 1EE99 for right bound
Normal Distribution
yields a probability density function value (only useful to plot the normal curve, in which case "normalpdf(x,μ,σ)
" is the variable)x
corresponds to P(left bound < X < right bound)normalcdf(left bound, right bound, μ, σ)
corresponds to P(left bound < Z < right bound) – standard normalnormalcdf(left bound, right bound)
yields the critical value, k: P(X < k) = pinvNorm(p,μ,σ)
yields the critical value, k: P(Z < k) = p for the standard normalinvNorm(p)
Student's tDistribution
yields the probability density function value (only useful to plot the studentt curve, in which case "tpdf(x,df)
" is the variable)x
corresponds to P(left bound < t < right bound)tcdf(left bound, right bound, df)
Chisquare Distribution
yields the probability density function value (only useful to plot the chi^{2} curve, in which case "Χ^{2}pdf(x,df)
" is the variable)x
corresponds to P(left bound < Χ^{2} < right bound)Χ^{2}cdf(left bound, right bound, df)
F Distribution
yields the probability density function value (only useful to plot the F curve, in which case "Fpdf(x,dfnum,dfdenom)
" is the variable)x
corresponds to P(left bound < F < right bound)Fcdf(left bound,right bound,dfnum,dfdenom)
Tests and Confidence Intervals
Access
STAT
and TESTS
.
For the confidence intervals and hypothesis tests, you may enter the data into the appropriate lists and press
DATA
to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT
once in the appropriate tests.
Confidence Intervals
is the confidence interval for mean when σ is known.ZInterval
is the confidence interval for mean when σ is unknown; s estimates σ.TInterval
is the confidence interval for proportion.1PropZInt
Hypothesis Tests
is the hypothesis test for single mean when σ is known.ZTest
is the hypothesis test for single mean when σ is unknown; s estimates σ.TTest
is the hypothesis test for two independent means when both σ's are known.2SampZTest
is the hypothesis test for two independent means when both σ's are unknown.2SampTTest
is the hypothesis test for single proportion.1PropZTest
is the hypothesis test for two proportions.2PropZTest
is the hypothesis test for independence.Χ^{2}Test
is the hypothesis test for goodnessoffit (TI84+ only).Χ^{2}GOFTest
is the hypothesis test for Linear Regression (TI84+ only).LinRegTTEST
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 Introductory Statistics
 Preface
 Sampling and Data
 Descriptive Statistics
 Introduction
 StemandLeaf Graphs (Stemplots), Line Graphs, and Bar Graphs
 Histograms, Frequency Polygons, and Time Series Graphs
 Measures of the Location of the Data
 Box Plots
 Measures of the Center of the Data
 Skewness and the Mean, Median, and Mode
 Measures of the Spread of the Data
 Descriptive Statistics
 Probability Topics
 Discrete Random Variables
 Introduction
 Probability Distribution Function (PDF) for a Discrete Random Variable
 Mean or Expected Value and Standard Deviation
 Binomial Distribution
 Geometric Distribution
 Hypergeometric Distribution
 Poisson Distribution
 Discrete Distribution (Playing Card Experiment)
 Discrete Distribution (Lucky Dice Experiment)
 Continuous Random Variables
 The Normal Distribution
 The Central Limit Theorem
 Confidence Intervals
 Hypothesis Testing with One Sample
 Hypothesis Testing with Two Samples
 The ChiSquare Distribution
 Linear Regression and Correlation
 F Distribution and OneWay ANOVA
 Appendix A: Review Exercises (Ch 313)
 Appendix B: Practice Tests (14) and Final Exams
 Appendix C: Data Sets
 Appendix D: Group and Partner Projects
 Appendix E: Solution Sheets
 Appendix F: Mathematical Phrases, Symbols, and Formulas
 Appendix G: Notes for the TI83, 83+, 84, 84+ Calculators
 Appendix H: Tables