Notes for the TI-83, 83+, 84, 84+ Calculators, Front matter | Statistics

Learning objectives

Quick Tips

Legend

View original figure (external; image not reproduced in this text edition)

Original figure description: A blank calculator button
represents a button press
[ ] represents yellow command or green letter behind a key
< > represents items on the screen

To adjust the contrast

Press

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.

, then hold

View original figure (external; image not reproduced in this text edition)

Original figure description: A white upward-pointing triangle is centered on a rounded rectangular blue button or icon, suggesting an 'up' action, 'upload', or 'collapse' function.

to increase the contrast or

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button with rounded corners features a prominent white downward-pointing triangle, typically indicating a dropdown menu, an expand function, or a scroll-down action.

to decrease the contrast.

To capitalize letters and words

Press

View original figure (external; image not reproduced in this text edition)

Original figure description: A light green rectangular button or badge with the word 'ALPHA' in bold, white, capitalized letters, accompanied by a subtle drop shadow.

to get one capital letter, or press

View original figure (external; image not reproduced in this text edition)

, then

View original figure (external; image not reproduced in this text edition)

Original figure description: A light green rectangular button or badge with the word 'ALPHA' in bold, white, capitalized letters, accompanied by a subtle drop shadow.

to set all button presses to capital letters. You can return to the top-level button values by pressing

View original figure (external; image not reproduced in this text edition)

Original figure description: A light green rectangular button or badge with the word 'ALPHA' in bold, white, capitalized letters, accompanied by a subtle drop shadow.

again.

To correct a mistake

If you hit a wrong button, press

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular gray button with a soft white glow around the edges features the word 'CLEAR' in bold, white, capital letters, suggesting a function to reset or remove content.

and start again.

To write in scientific notation

Numbers in scientific notation are expressed on the TI-83, 83+, 84, and 84+ using E notation, such that...

4.321 E 4 = $4 .321 \times 10^{4}$
4.321 E –4 = $4 .321 \times 10^{–4}$

To transfer programs or equations from one calculator to another

Both calculators: Insert your respective end of the link cable cable and press

View original figure (external; image not reproduced in this text edition)

, then [LINK].

Calculator receiving information

Use the arrows to navigate to and select <RECEIVE>.
Press
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.

Calculator sending information

Press the appropriate number or letter.
Use the up and down arrows to access the appropriate item.
Press
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
to select the item to transfer.
Press the right arrow to navigate to and select <TRANSMIT>.
Press
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.

Both calculators—Insert your respective end of the link cable, press

View original figure (external; image not reproduced in this text edition)

, then [QUIT] to exit when done.

Manipulating One-Variable Statistics

We are manipulating one-variable statistics.

Sample Data
Data	Frequency
–2	10
–1	3
0	4
1	5
3	8

To begin

Turn on the calculator.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark grey rectangular button with rounded corners displays the word 'ON' in bright white, bold capital letters, indicating an activated state or selection.
Access statistics mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.
Select <4:ClrList> to clear data from lists, if desired.

View original figure (external; image not reproduced in this text edition)

Original figure description: A light gray button featuring the number '4' in black text, against a dark gray background at the bottom. The button has softly rounded corners.
, then
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Enter the list [L1] to be cleared.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L1] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Display the last instruction.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [ENTRY].
Continue clearing any remaining lists in the same fashion, if desired.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button features a white triangle pointing left, commonly used as a 'previous' or 'back' navigation icon.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L2] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Access statistics mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.
Select <1:Edit . . .>.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Enter data. Data values go into [L1]. (You may need to arrow over to [L1]).
- Type in a data value and enter it. For negative numbers, use the negate key at the bottom of the keypad.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A close-up of a gray button or icon featuring a minus sign enclosed in parentheses, typically used to indicate collapsing, minimizing, or subtracting an item.
  ,
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A close-up shot of a rectangular grey button featuring the number 9 prominently displayed in its center.
  ,
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
  .
- Continue in the same manner until all data values are entered.
In [L2], enter the frequencies for each data value in [L1].
- Type in a frequency and enter it. If a data value appears only once, the frequency is 1.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A light gray button featuring the number '4' in black text, against a dark gray background at the bottom. The button has softly rounded corners.
  ,
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
  .
- Continue in the same manner until all data values are entered.
Access statistics mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.
Navigate to <CALC>.
Access <1:1-var Stats>.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Indicate that the data is in [L1]...

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L1] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rounded rectangular button features a single white comma symbol in its center, set against a dark background.
,
...and indicate that the frequencies are in [L2].

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L2] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
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 built-in [STAT PLOT] application. In the first method, we will use the default ZOOM. The second method will involve customizing a new graph.

Access graphing mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [STAT PLOT].
Select <1:plot 1> to access plotting - first graph.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Use the arrows to navigate to <ON> to turn on Plot 1.
<ON> ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Use the arrows to go to the histogram picture and select the histogram.
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Use the arrows to navigate to <Xlist>.
If [L1] is not selected, select it.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L1] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Use the arrows to navigate to <Freq>.
Assign the frequencies to [L2].

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L2] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Go back to access other graphs.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [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.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue button with rounded corners displaying the white, glowing text 'Y='.
Select each equal sign (=).

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button with rounded corners features a prominent white downward-pointing triangle, typically indicating a dropdown menu, an expand function, or a scroll-down action.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Continue until all equations are deselected.

To clear equations

Access the list of equations.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue button with rounded corners displaying the white, glowing text 'Y='.
Use the arrow keys to navigate to the right of each equal sign (=) and clear them.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button with rounded corners features a prominent white downward-pointing triangle, typically indicating a dropdown menu, an expand function, or a scroll-down action.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular gray button with a soft white glow around the edges features the word 'CLEAR' in bold, white, capital letters, suggesting a function to reset or remove content.
.
Repeat until all equations are deleted.

To draw default histogram

Access the ZOOM menu.

View original figure (external; image not reproduced in this text edition)

Original figure description: ZOOM key
Select <9:ZoomStat>.

View original figure (external; image not reproduced in this text edition)

Original figure description: A close-up shot of a rectangular grey button featuring the number 9 prominently displayed in its center.
The histogram will display with a window automatically set.

To draw a custom histogram

Access window mode to set the graph parameters.

View original figure (external; image not reproduced in this text edition)
Original figure description: window key
- $X_{\min} = –2.5$
- $X_{\max} = 3.5$
- $X_{s c l} = 1$ (width of bars)
- $Y_{\min} = 0$
- $Y_{\max} = 10$
- $Y_{s c l} = 1$ (spacing of tick marks on y-axis)
- $X_{r e s} = 1$
Access graphing mode to see the histogram.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button with a slight shadow, featuring the word 'GRAPH' in bright, glowing white text. The text has a soft, diffused light effect against the blue background.

To draw box plots

Access graphing mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [STAT PLOT].
Select <1:Plot 1> to access the first graph.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Use the arrows to select <ON> and turn on Plot 1.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Use the arrows to select the box plot picture and enable it.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Use the arrows to navigate to <Xlist>.
If [L1] is not selected, select it.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L1] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Use the arrows to navigate to <Freq>.
Indicate that the frequencies are in [L2].

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L2] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Go back to access other graphs.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [STAT PLOT].
Be sure to deselect or clear all equations before graphing using the method mentioned above.
View the box plot.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button with a slight shadow, featuring the word 'GRAPH' in bright, glowing white text. The text has a soft, diffused light effect against the blue background.
, [STAT PLOT].

Linear Regression

Sample Data

The following data are real. The percent of declared ethnic minority students at De Anza College for selected years from 1970–1995 is indicated in the following table.

The independent variable is Year, while the independent variable is Student Ethnic Minority Percentage.

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%

Student Ethnic Minority Percentage

View original figure (external; image not reproduced in this text edition)

Original figure description: This is a scatterplot for the data provided. Year is plotted on the horizontal axis and percent is plotted on the vertical axis. The points show a strong, curved, upward trend.

By hand, verify the scatterplot above.

To enter data and perform linear regression

ON Turns calculator on.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark grey rectangular button with rounded corners displays the word 'ON' in bright white, bold capital letters, indicating an activated state or selection.
Before accessing this program, be sure to turn off all plots.
- Access graphing mode.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
  , [STAT PLOT].
- Turn off all plots.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A light gray button featuring the number '4' in black text, against a dark gray background at the bottom. The button has softly rounded corners.
  ,
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
  .
Round to three decimal places.
- Access the mode menu.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular gray button with rounded corners, featuring the white, slightly blurred text 'MODE' centered on its surface.
  , [STAT PLOT].
- Navigate to <Float> and then to the right until you reach <3>.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A blue rectangular button with rounded corners features a prominent white downward-pointing triangle, typically indicating a dropdown menu, an expand function, or a scroll-down action.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.
  .
- All numbers will be rounded to three decimal places until changed.
  
  View original figure (external; image not reproduced in this text edition)
  
  Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Enter statistics mode and clear lists [L1] and [L2], as described previously.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A light gray button featuring the number '4' in black text, against a dark gray background at the bottom. The button has softly rounded corners.
.
Enter editing mode to insert values for x and y.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Enter each value. Press
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
to continue.

To display the correlation coefficient

Access the catalog.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [CATALOG].
Arrow down and select <DiagnosticOn>.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button with rounded corners features a prominent white downward-pointing triangle, typically indicating a dropdown menu, an expand function, or a scroll-down action.
... ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
$r$ and $r
2$ will be displayed during regression calculations.
Access linear regression.

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray rectangular button with rounded corners displays the word 'STAT' in prominent, glowing white capital letters, suggesting an urgent or immediate action.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.
.
Select the form of y = a + bx.

View original figure (external; image not reproduced in this text edition)

Original figure description: A light grey rectangular button or tab displays the number '8' in a darker shade of grey, possibly indicating a count or selection. The object has slightly rounded corners and a subtle shadow underneath, suggesting depth.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.

The display will show the following information

LinReg

y = a + bx
a = –3176.909
b = 1.617
r² = 0.924
r = 0.961

This means the Line of Best Fit (Least Squares Line) is:

y = –3176.909 + 1.617x
% = –3176.909 + 1.617 (year #)

The correlation coefficient is r = 0.961.

To see the scatter plot

Access graphing mode.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [STAT PLOT].
Select <1:Plot 1> To access plotting - first graph.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Navigate and select <ON> to turn on <1:Plot 1>.
<ON>
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Navigate to the first picture.
Select the scatter plot.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Navigate to <Xlist>.
If [L1] is not selected, press
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, then [L1] to select it.
Confirm that the data values are in [L1].
<ON>,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Navigate to <Ylist>.
Select that the frequencies are in [L2].

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L2] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Go back to access other graphs.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [STAT PLOT]
Use the arrows to turn off the remaining plots.
Access window mode to set the graph parameters.

View original figure (external; image not reproduced in this text edition)

Original figure description: window key
- $X_{\min} = 1970$
- $X_{\max} = 2000$
- $X_{s c l} = 10$ (spacing of tick marks on x-axis)
- $Y_{\min} = - 0.05$
- $Y_{\max} = 60$
- $Y_{s c l} = 10$ (spacing of tick marks on y-axis)
- $X_{r e s} = 1$
Be sure to deselect or clear all equations before graphing, using the instructions above.
Press the graph button to see the scatter plot.
View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button with a slight shadow, featuring the word 'GRAPH' in bright, glowing white text. The text has a soft, diffused light effect against the blue background.

To see the regression graph

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

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue button with rounded corners displaying the white, glowing text 'Y='.
Access the vars menu and navigate to <5: Statistics>.

View original figure (external; image not reproduced in this text edition)

Original figure description: vars key
,
View original figure (external; image not reproduced in this text edition)

Original figure description: number 5 key
.
Navigate to <EQ>.
<1: RegEQ> contains the regression equation which will be entered in Y1.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
Press the graphing mode button. The regression line will be superimposed over the scatter plot.

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button with a slight shadow, featuring the word 'GRAPH' in bright, glowing white text. The text has a soft, diffused light effect against the blue background.

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.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [LIST], then <RESID>.
Press enter twice to view the list of residuals. Use the arrows to select them.

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
The critical point for an outlier is 1.9 V SSE n 2 , where
- $n$ = number of pairs of data
- $SSE$ = sum of the squared errors
- $residual
  2$
Store the residuals in [L3].

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray button displaying the word 'STOP' next to a white play symbol, suggesting a media control or a stop/start function.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L3] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Calculate the $(residual)
2

n
2$ . Note that $n
2

8$ .

View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L3] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: x-squared key
,
View original figure (external; image not reproduced in this text edition)

Original figure description: division key
, then
View original figure (external; image not reproduced in this text edition)

Original figure description: A light grey rectangular button or tab displays the number '8' in a darker shade of grey, possibly indicating a count or selection. The object has slightly rounded corners and a subtle shadow underneath, suggesting depth.
.
Store this value in [L4].

View original figure (external; image not reproduced in this text edition)

Original figure description: A dark gray button displaying the word 'STOP' next to a white play symbol, suggesting a media control or a stop/start function.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L4] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Calculate the critical value using the equation above.

View original figure (external; image not reproduced in this text edition)

Original figure description: A light gray, horizontally elongated rectangular button with softly rounded corners features a prominent dark gray numeral '1' centered on its surface. It resembles a counter, a step indicator, or a label.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: decimal point key
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A close-up shot of a rectangular grey button featuring the number 9 prominently displayed in its center.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A close-up of a digitally rendered blue button with a soft glow, featuring a white 'X' symbol in the center, indicating a close or cancel function.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [V] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [LIST]
View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A blue rectangular button features a prominent white triangular play icon, commonly used to initiate video or audio playback.
,
View original figure (external; image not reproduced in this text edition)

Original figure description: number 5 key
,
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular yellow button or banner with a subtle gradient and shadow effect, displaying the text '2nd' in prominent, glowing white letters. The text has a slightly blurred or soft-focus appearance.
, [L4] ,
View original figure (external; image not reproduced in this text edition)

Original figure description: closing parenthesis key
,
View original figure (external; image not reproduced in this text edition)

Original figure description: closing parenthesis key
, then
View original figure (external; image not reproduced in this text edition)

Original figure description: A rectangular blue button with rounded corners features the word 'ENTER' in white, glowing capital letters. There's a subtle drop shadow beneath the button, giving it a three-dimensional effect.
.
Verify that the calculator displays 7.642669563. This is the critical value.
Compare the absolute value of each residual value in [L3] 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.

To obtain estimates of y for various x-values

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

View original figure (external; image not reproduced in this text edition)

Original figure description: A blue, rounded rectangular button with the word 'TRACE' in glowing white text, suggesting a digital control or function.

on the graph of the regression line.

TI-83, 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

binompdf(n,p,x) corresponds to P(X = x)
binomcdf(n,p,x) corresponds to P(X ≤ x)
To see a list of all probabilities for x: 0, 1, . . . , n, leave off the "x" parameter.

Poisson Distribution

poissonpdf(λ,x) corresponds to P(X = x)
poissoncdf(λ,x) corresponds to P(X ≤ x)

Continuous Distributions (general)

$- \infty$ uses the value –1EE99 for left bound
uses the value 1EE99 for right bound

Normal Distribution

normalpdf(x,μ,σ) yields a probability density function value, only useful to plot the normal curve, in which case "x" is the variable
normalcdf(left bound, right bound, μ, σ) corresponds to P(left bound < X < right bound)
normalcdf(left bound, right bound) corresponds to P(left bound < Z < right bound) – standard normal
invNorm(p,μ,σ) yields the critical value, k: P(X < k) = p
invNorm(p) yields the critical value, k: P(Z < k) = p for the standard normal

Student's t-Distribution

tpdf(x,df) yields the probability density function value, only useful to plot the student-t curve, in which case "x" is the variable)
tcdf(left bound, right bound, df) corresponds to P(left bound < t < right bound)

Chi-square Distribution

Χ²pdf(x,df) yields the probability density function value, only useful to plot the chi² curve, in which case "x" is the variable
Χ²cdf(left bound, right bound, df) corresponds to P(left bound < Χ² < right bound)

F Distribution

Fpdf(x,dfnum,dfdenom) yields the probability density function value, only useful to plot the F curve, in which case "x" is the variable
Fcdf(left bound,right bound,dfnum,dfdenom) corresponds to P(left bound < F < right bound)

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

ZInterval is the confidence interval for mean when σ is known.
TInterval is the confidence interval for mean when σ is unknown; s estimates σ.
1-PropZInt is the confidence interval for proportion.

Hypothesis Tests

Z-Test is the hypothesis test for single mean when σ is known.
T-Test is the hypothesis test for single mean when σ is unknown; s estimates σ.
2-SampZTest is the hypothesis test for two independent means when both σs are known.
2-SampTTest is the hypothesis test for two independent means when both σs are unknown.
1-PropZTest is the hypothesis test for a single proportion.
2-PropZTest is the hypothesis test for two proportions.
Χ²-Test is the hypothesis test for independence.
Χ²GOF-Test is the hypothesis test for goodness-of-fit (TI-84+ only).
LinRegTTEST is the hypothesis test for Linear Regression (TI-84+ only).

Attribution. Statistics, OpenStax, Rice University, and the contributing authors credited in the book. Licensed under Creative Commons Attribution 4.0 International. Source revision 7dea80ae28 of openstax/osbooks-statistics (2026-04-23). CC BY 4.0. Original source ↗. Text edition of a pinned CC BY 4.0 source revision of the OpenStax book, converted from CNXML by the EvidenceHelix importer. Original prose, learning objectives, tables, exercises, glossary and captions are preserved; images are not copied (figures link to the original source and keep their credits). No new content was added. Later revisions of this book can carry different licence terms and are not used.