To calculate RSD on a TI-84 Plus, enter your data in list L1, run 1-Var Stats, and divide the sample standard deviation by the mean: RSD = Sx ÷ x̄ × 100. For seven tablet masses with x̄ = 250.1428571 mg and Sx = 1.729023947 mg, the result is 0.69%. You can also get the answer in one line by typing stdDev(L1)/mean(L1)*100 on the home screen.
The steps below follow Texas Instruments’ TI-84 Plus guidebook and support articles. They apply to the TI-84 Plus, TI-84 Plus Silver Edition and TI-84 Plus CE, with the display differences noted where they matter.
Quick Steps
- Press STAT 1 to open the list editor.
- Clear L1 if it holds old data, then type each value followed by ENTER.
- Press 2nd QUIT to return to the home screen.
- Press STAT ► 1 to choose 1-Var Stats, set List to L1, and select Calculate.
- Read x̄ (mean) and Sx (sample standard deviation).
- Calculate Sx ÷ x̄ × 100, ideally by recalling the stored values instead of retyping them.
The rest of this guide explains each step, including what to do when the screens look different on your model.
Step 1: Clear Old Data From L1
The TI-84 keeps list data until you delete it, so a list often still holds numbers from a previous problem. Mixing old and new values is the most common cause of a wrong RSD.
To clear L1 in the list editor, press STAT 1, press ▲ until the cursor sits on the L1 name at the top of the column, then press CLEAR ENTER. The column empties but stays in the editor.
Two other documented options:
- ClrList: press STAT 4 to paste
ClrList, add the list name with 2nd L1, and press ENTER. - ClrAllLists: press 2nd MEM and choose 4:ClrAllLists. This empties every list in memory, so use it only if you do not need the others.
Don’t press DEL on a list name. The guidebook explains that DEL on a list name removes the list from the editor without deleting it from memory. If L1 has disappeared from your editor, press STAT 5 to paste SetUpEditor and press ENTER. That restores L1 through L6 to the first six columns.
Step 2: Enter the Data
With the cursor in the first row of L1, type each value and press ENTER after it. The cursor moves down one row each time.
This guide uses seven tablet masses in mg:
| Row | L1 |
|---|---|
| 1 | 251.3 |
| 2 | 248.7 |
| 3 | 250.2 |
| 4 | 252.8 |
| 5 | 249.5 |
| 6 | 250.9 |
| 7 | 247.6 |
To fix a mistake, move the cursor onto the wrong value and type the correct one over it. When the list is complete, count the rows. The number of values will appear as n in the results, and checking it catches missed or doubled entries.
Press 2nd QUIT to return to the home screen.
Step 3: Run 1-Var Stats
Press STAT, then ► to move to the CALC menu, and press 1 for 1-Var Stats. What happens next depends on your operating system and settings.
With Stat Wizards on (TI-84 Plus OS 2.55MP or later, and the TI-84 Plus CE). A setup screen appears with three lines:
- List: make sure it says L1. If not, enter it with 2nd L1.
- FreqList: leave this blank for ordinary data.
- Calculate: move down to it and press ENTER.
TI’s support article on one-variable statistics notes that Stat Wizards are on by default.
With Stat Wizards off, or on an older operating system. The command 1-Var Stats is pasted onto the home screen. Press ENTER. If you do not name a list, the calculator uses L1, but you can type 2nd L1 before ENTER to be explicit.
To switch the wizards on or off, press MODE, scroll down to STAT WIZARDS, highlight ON or OFF, and press ENTER.
Step 4: Read x̄, Sx and σx
The results screen lists the statistics in this order. Press ▼ to scroll to the lower lines.
| Label | Meaning | Tablet example |
|---|---|---|
| x̄ | Mean | 250.1428571 |
| Σx | Sum of the values | 1751 |
| Σx² | Sum of the squared values | 438018.08 |
| Sx | Sample standard deviation (n − 1) | 1.729023947 |
| σx | Population standard deviation (n) | 1.600765123 |
| n | Number of values | 7 |
| minX, Q1, Med, Q3, maxX | Five-number summary | 247.6, 248.7, 250.2, 251.3, 252.8 |
TI’s knowledge base states the difference directly: Sx uses n − 1 as the denominator and σx divides by n.
For RSD of replicate measurements, experimental data or any sample drawn from a larger group, use Sx. Use σx only when the list is the entire population you want to describe. The sample vs population standard deviation guide explains the choice in more detail.
Step 5: Calculate %RSD
There are three ways to finish. The second and third avoid rounding errors from copying numbers off the screen.
Option A: Type the displayed values
Clear the results with CLEAR and type:
1.729023947 ÷ 250.1428571 × 100
The answer is 0.6912145991, so the RSD is 0.69%. This works, but typing shortened values such as 1.73 ÷ 250 × 100 gives 0.692, which is slightly off. Copy all the digits if you use this method.
Option B: Recall Sx and x̄ from the VARS menu
After 1-Var Stats has run, the calculator stores each result as a variable. The guidebook explains that pressing VARS and selecting 5:Statistics opens the statistics variables, with x̄, Sx and σx on the XY menu.
- Press VARS 5, then choose Sx from the XY menu. It is pasted to the home screen.
- Press ÷.
- Press VARS 5 again and choose x̄.
- Press × 1 0 0 ENTER.
The screen shows Sx/x̄*100 and the result 0.6912145991. No parentheses are needed, because the TI-84 evaluates multiplication and division from left to right. For a population RSD, choose σx instead of Sx. TI’s variance support article confirms that σx is item 4 on this menu.
Option C: One line with stdDev( and mean(
This option does not need 1-Var Stats at all. Press 2nd LIST and ◄ to open the MATH menu, where 3:mean( and 7:stdDev( are listed. Build this expression:
stdDev(L1)/mean(L1)*100
Press ENTER to get 0.6912145991 again. The stdDev( function returns the sample standard deviation. The guidebook’s own example, stdDev({1,2,5,-6,3,-2}) = 3.937003937, matches the n − 1 formula exactly. There is no population version on that menu, so use σx from 1-Var Stats if you need a population RSD.
Several Samples at Once
The TI-84 has six named lists, L1 to L6, so you can keep replicates for different samples side by side. Enter the first sample in L1, the second in L2 and so on. The one-line method then works for each list by changing the list name:
stdDev(L2)/mean(L2)*100
With 1-Var Stats, set the List line to L2 in the wizard, or type 1-Var Stats L2 on the home screen. Remember that Sx and x̄ in the VARS menu always refer to the most recent 1-Var Stats run, so recall them before running the next list.
Repeated values and frequency lists
If your data contains repeated values, you can enter each distinct value once in L1 and its count in L2, then set FreqList to L2. The guidebook requires every frequency to be zero or more, with at least one above zero. Keep the frequencies to whole numbers: with non-integer frequencies the calculator does not display Sx, so a sample RSD is not available.
Check Your Setup With TI’s Own Example
The TI-84 Plus guidebook uses twelve pendulum string lengths in its getting-started chapter: 6.5, 11.0, 13.2, 15.0, 18.0, 23.1, 24.4, 26.6, 30.5, 34.3, 37.6 and 41.5 cm. Its 1-Var Stats screen shows x̄ = 23.475, Sx = 11.08997295 and σx = 10.61784073.
Entering those values and following the steps above should give:
If your screen shows the same x̄, Sx and σx, your list and settings are correct. The large RSD reflects the fact that these are different string lengths, not repeat measurements of one length, so the example checks your method rather than representing a precision result.
Display Problems: Fractions and Rounded Answers
Two MODE settings change how the RSD appears without changing the underlying value.
- Answers. On the TI-84 Plus, the MODE screen’s Answers setting offers AUTO, DEC and FRAC. With FRAC, a result that has an exact fraction form may appear as one. Press MATH and choose ►Dec to convert it, or set Answers to DEC. The TI-84 Plus CE guide lists AUTO and DEC for this setting.
- Float or Fix. If the MODE screen is set to a fixed number of decimal places, answers are rounded on screen. An RSD of 0.6912145991 would show as 0.69 in Fix 2. Choose FLOAT to see all digits.
Round only the final RSD. Rounding x̄ or Sx before dividing is the usual reason a hand-calculated answer differs from the calculator.
Common TI-84 Errors and Fixes
The error names below are from TI’s documentation. The TI-84 Plus CE shows DIM MISMATCH as DIMENSION MISMATCH.
| Message or symptom | What it means | Fix |
|---|---|---|
| ERR:DIM MISMATCH | Two lists used together have different lengths, often because FreqList was filled in by mistake | Leave FreqList blank in the wizard, or remove the frequency list from the command |
| ERR:STAT | The statistics calculation is not valid for the list, for example it has fewer than two data points | Check that L1 holds at least two values |
| ERR:UNDEFINED | A statistics variable such as Sx was recalled before 1-Var Stats ran, or after the list was edited | Run 1-Var Stats again, then recall the variables |
| ERR:SYNTAX | A typing error, such as a missing parenthesis in stdDev(L1) | Retype the expression |
| ERR:INVALID DIM | Often a stat plot is switched on for an empty list | Press 2nd STAT PLOT and choose PlotsOff |
| L1 missing from the editor | The list name was removed with DEL | Run SetUpEditor (STAT 5 ENTER) |
| Sx is blank | A frequency list with non-integer values was used | Remove the frequency list or use whole-number frequencies |
| RSD looks wrong but no error | Old values left in L1, or 1-Var Stats run on a different list | Check n and the list name, then recalculate |
The guidebook notes that editing a list clears all statistics variables. That protects you from stale Sx values after an edit, but not from reading results for the wrong list, so glance at n every time.
TI-84 Plus and TI-84 Plus CE: What Differs
The RSD workflow is the same on both. The documented differences are cosmetic or relate to settings:
| Feature | TI-84 Plus (OS 2.55MP) | TI-84 Plus CE |
|---|---|---|
| Key legends | Uppercase (STAT, ENTER) | Lowercase (stat, enter) |
| Stat Wizards | Introduced in OS 2.55MP, on by default | Available; switch on or off on the MODE screen |
| Answers setting | AUTO, DEC, FRAC | AUTO, DEC |
| Error name | ERR:DIM MISMATCH | DIMENSION MISMATCH |
The TI-84 Plus Silver Edition follows the same guidebook as the TI-84 Plus. The TI-83 Plus uses the same STAT EDIT and STAT CALC menus but has no Stat Wizards, so 1-Var Stats always pastes to the home screen.
Verify With the RSD Calculator
Enter the same values in the RSD Calculator, choose Sample (n − 1), and compare the mean, standard deviation and %RSD with your TI-84 screen. The calculator also shows each step of the working, which helps if the two disagree.
If you use a non-graphing scientific calculator instead, the process is similar but the menus differ. How to Calculate RSD on a Scientific Calculator covers the general workflow, including calculators without a statistics mode.
Frequently Asked Questions
Should I use Sx or σx for RSD on a TI-84?
Use Sx for replicate measurements and most lab or survey data, because it is the sample standard deviation (dividing by n − 1). Use σx, the population standard deviation (dividing by n), only when your list contains every value in the population you are describing.
Does the TI-84 have an RSD or coefficient of variation function?
No. 1-Var Stats reports the mean, sums, both standard deviations, n and the five-number summary, but not RSD or CV. You calculate it yourself as Sx ÷ x̄ × 100, or in one line with stdDev(L1)/mean(L1)*100.
Why does my TI-84 show ERR:UNDEFINED when I recall Sx?
The statistics variables only hold values after 1-Var Stats has been run, and they are cleared when you edit a list. Run 1-Var Stats again on your data list, then recall Sx and x̄.
Why did my RSD answer come out as a fraction?
On models with a FRAC answer setting, the calculator may show an exact fraction when one exists. Press MATH and choose ►Dec to convert the last answer to a decimal, or set the Answers option on the MODE screen to DEC.
Is stdDev( on the TI-84 the sample or population standard deviation?
It returns the sample standard deviation, the same value as Sx. The example in TI's own guidebook, stdDev({1,2,5,-6,3,-2}) = 3.937003937, matches the n − 1 formula. For a population RSD, use σx from 1-Var Stats instead.
