From a Data Table to a TI-84 Scatterplot
In “Constructing a Scatterplot by Hand,” you learned to keep each observational unit’s measurements together as one point \((x,y)\). A TI-84 can plot those points quickly, but it still depends on you to enter the pairs in the right order, assign the correct list to each axis, and choose a useful viewing window.
For this tutorial, \(x\) is the explanatory variable and belongs on the horizontal axis. The response variable, \(y\), belongs on the vertical axis. We will store the \(x\)-values in list L1 and the corresponding \(y\)-values in L2. The lists must match by position: the first value in L1 is paired with the first value in L2, the second with the second, and so on.
Enter the Paired Values
Press STAT, choose 1:Edit, and press ENTER to open the list editor. If you see old values, clear the lists you plan to use before entering a new data set. Move the cursor to the L1 heading, press CLEAR, then press ENTER. Repeat for L2. This clears the list contents without deleting the list itself.
Move the cursor to the first blank cell beneath L1 and type the explanatory-variable values, pressing ENTER after each value. Then enter the response-variable values beneath L2 in the same row order as their matching \(x\)-values. If the first row of your data table is \((x_1,y_1)\), enter \(x_1\) first in L1 and \(y_1\) first in L2.
A reliable habit is to read across the original data table one row at a time and enter each pair before moving to the next row. When you finish, check that L1 and L2 have the same number of entries and that every row still matches its original pair. Sorting one list without making the same change to the other list breaks the pairings.
Set Up STAT PLOT
To configure a scatterplot, press 2nd, then Y= to open STAT PLOT. Choose Plot1 (or another plot number you intend to use). In the setup screen, turn the plot on, select the scatterplot icon, set Xlist to L1, set Ylist to L2, and choose a point mark that is easy to see.
On a TI-84, the list shortcut for L1 is 2nd, then 1; the shortcut for L2 is 2nd, then 2. To change a list field, move the cursor to that field, select or enter the intended list, and press ENTER if needed. The scatterplot icon is the one showing separate dots, not a connected-line display.
Press 2nd, then Y=, and choose the plot number you want to configure.
Select On so the calculator will display this plot.
Select the scatterplot icon, set Xlist to L1 and Ylist to L2, and choose a visible point mark.
Use ZoomStat or set a window, then check that the points correspond to the entered pairs.
The Xlist and Ylist settings determine which lists supply the horizontal and vertical coordinates. If those settings are reversed, the calculator plots the same paired numbers with the variables swapped. If another STAT PLOT is also turned on, its marks may appear in the same graph and make the display confusing. When you are unsure, check that only the intended plot is on.
Use ZoomStat or Set a Window
After configuring STAT PLOT, press ZOOM and choose 9:ZoomStat. ZoomStat adjusts the viewing window to include the data in the active statistical plots. The calculator then displays the scatterplot. The exact window limits may include extra space around the points; that margin can make the graph easier to read.
If the graph is blank or points are cut off, ZoomStat is a useful first step. If you need particular axis limits or want a specific scale, set the window yourself. Press WINDOW and enter values for Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl. Xmin and Xmax set the horizontal range; Ymin and Ymax set the vertical range. Xscl and Yscl control the spacing of the axis marks.
Choose limits that include every data value and intervals that make the axes readable. The two axes can use different ranges and intervals because the variables may have different units. After entering a manual window, press GRAPH. If a point is missing, check the ranges first: it may be outside the window even though its data are correctly stored.
Worked Example: Plotting Processor Load and Fan Speed
A fictional technician tests a small computer under several processor loads. The explanatory variable is processor load, \(x\), in percent. Fan speed is the response variable, \(y\), in revolutions per minute (rpm). Enter the values below as paired observations.
| Test | Processor load (%) | Fan speed (rpm) |
|---|---|---|
| 1 | 10 | 820 |
| 2 | 20 | 900 |
| 3 | 30 | 980 |
| 4 | 40 | 1080 |
| 5 | 50 | 1170 |
| 6 | 60 | 1260 |
| 7 | 70 | 1370 |
Enter the lists. In the list editor, enter 10, 20, 30, 40, 50, 60, and 70 in L1. Enter 820, 900, 980, 1080, 1170, 1260, and 1370 in L2 in that order. For example, the fourth pair is \((40,1080)\): the fourth L1 entry and fourth L2 entry make the point for Test 4.
Configure and draw. Turn Plot1 on, select the scatterplot icon, set Xlist to L1 and Ylist to L2, and select a dot mark. Press ZOOM and choose 9:ZoomStat. The calculator displays one point for each of the seven tests.
Choose a manual window if useful. To use a specified window, enter Xmin = 0, Xmax = 80, Xscl = 10, Ymin = 700, Ymax = 1500, and Yscl = 100 in the WINDOW screen. Press GRAPH. These limits include the smallest and largest values in both lists, with space around the data. The horizontal scale is in processor-load percentage points, and the vertical scale is in rpm.
Check the display. Use TRACE to move among plotted points and read their displayed coordinates. Confirm, for example, that one point is \((40,1080)\), not \((1080,40)\). The graph should show seven plotted pairs, matching the seven rows in the table.
Worked Example: Choosing a Window for Rainfall and Stream Turbidity
For an invented environmental monitoring exercise, a student records rainfall intensity and stream turbidity at several observation times. Rainfall intensity is \(x\), in millimeters per hour; turbidity is \(y\), in measurement units used by the fictional monitoring activity. The goal here is to display the paired values.
| Observation | Rainfall intensity (mm/hour) | Turbidity (units) |
|---|---|---|
| A | 18 | 3.2 |
| B | 23 | 4.1 |
| C | 27 | 4.5 |
| D | 31 | 5.7 |
| E | 36 | 6.1 |
| F | 41 | 7.8 |
| G | 47 | 8.9 |
Enter and assign the lists. Put 18, 23, 27, 31, 36, 41, and 47 in L1. Put 3.2, 4.1, 4.5, 5.7, 6.1, 7.8, and 8.9 in L2. Set Xlist to L1 and Ylist to L2. This assignment puts rainfall on the horizontal axis and turbidity on the vertical axis.
Try ZoomStat. Turn on the scatterplot and use ZoomStat to bring all the values into view. If the automatic range is suitable for your purpose, you can use that graph. ZoomStat is not a requirement to use a particular axis start; it is a quick way to fit the data in the viewing screen.
Set a deliberate manual window. For a graph with clear tick intervals, enter Xmin = 10, Xmax = 50, Xscl = 5, Ymin = 2, Ymax = 10, and Yscl = 1. Press GRAPH. The rainfall values from 18 to 47 all lie within the horizontal range, and the turbidity values from 3.2 to 8.9 all lie within the vertical range. The display uses different intervals on the two axes because the variables have different units and numerical ranges.
Verify the plotted pairs. Use TRACE or compare visible coordinates with the table. Observation A should appear at approximately \((18,3.2)\), and Observation G at approximately \((47,8.9)\). If the values appear outside the graph, check the window limits before changing the entered data.
Worked Example: Finding a Pairing Error Before Plotting
A fictional consumer-technology club measures file size and download time for six test files. File size is \(x\), in megabytes, and download time is \(y\), in seconds. A student has entered the file sizes in order but accidentally entered the download times in a different order.
| File | File size (MB) | Download time (seconds) |
|---|---|---|
| A | 5 | 12 |
| B | 10 | 18 |
| C | 15 | 21 |
| D | 20 | 28 |
| E | 25 | 31 |
| F | 30 | 39 |
Audit the list entries. The correct L1 entries are 5, 10, 15, 20, 25, and 30. The correct L2 entries are 12, 18, 21, 28, 31, and 39 in the same row order. Suppose the student’s L2 instead reads 12, 21, 18, 28, 31, 39. The second and third times have been switched, so the calculator would plot \((10,21)\) and \((15,18)\), not the intended points \((10,18)\) and \((15,21)\).
Correct the entries before drawing. Return to STAT, choose Edit, and replace the second and third values in L2 with 18 and 21, respectively. Check each entry against its row in the source table. Then confirm Plot1 is on, Xlist is L1, and Ylist is L2. Use ZoomStat or set a window such as Xmin = 0, Xmax = 35, Xscl = 5, Ymin = 0, Ymax = 45, and Yscl = 5. Press GRAPH to display the corrected pairs.
Check the plotted result. There should be six points. TRACE can help inspect their coordinates, but the original table is the authority for whether the pairings are correct. A calculator will faithfully plot the lists it receives, even when an entry error has made those lists represent the wrong pairs.
Common Mistakes and AP Exam Tips
- Putting the variables in the wrong lists: L1 should contain the explanatory-variable values and L2 the corresponding response-variable values when using the setup in this tutorial. Check the Xlist and Ylist fields, not just the list contents.
- Entering matching values in different orders: The calculator pairs entries by position. Keep the original table’s row order, and do not sort one list independently.
- Forgetting to turn the plot on: A correctly filled list does not appear as a graph if the selected STAT PLOT is off. Check the plot’s On setting.
- Using the wrong display icon: Select the icon with separate dots for a scatterplot. A different plot type will not show the paired observations as the intended scatterplot.
- Assuming a blank screen means the data are gone: The viewing window may not include the data. Try ZoomStat, then inspect or set the WINDOW values.
- Leaving other plots on: An additional active plot can add unexpected marks. Check the STAT PLOT menu and turn off plots you are not using.
- Trusting the calculator instead of checking the data: Use the table to verify list order and selected coordinates. The calculator does not know whether a pair was entered correctly.
For clear communication on an AP Statistics task, identify which variable is on each axis and explain that matching list entries form the plotted pairs. When asked to construct the graph, make sure the scatterplot displays all the observations and uses readable, labeled axes. The calculator is a tool for drawing; it does not replace checking that the data and settings represent the intended variables.
Check Your Understanding
Answer each question using the TI-84 plotting steps in this tutorial.
- A table lists temperature as the explanatory variable and power use as the response variable. Which values belong in L1 and L2, and what should the Xlist and Ylist settings be?
- Explain why the first entry in L1 must stay paired with the first entry in L2. What kind of error can result from sorting only one list?
- After the lists are entered and the scatterplot is configured, what does ZoomStat do? When might you choose to set WINDOW values manually instead?
- A graph screen is blank even though you entered data. Name two plot or window settings you would check.
- For observations \((12,4.5)\) and \((18,6.2)\), describe how the values should be entered in L1 and L2 and which coordinates the calculator should plot.