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How to find standard deviation on a TI-84
Enter the data into L1, run 1-Var Stats, and read Sx for a sample or σx for a population. Full keystrokes below, including the frequency-list variant and the two mistakes that account for most wrong answers.
The keystrokes
- Clear the old list. STAT → 4:ClrList → 2nd 1 (which types L1) → ENTER. Skipping this is the single most common cause of a wrong answer, because leftover values from the last problem stay in the list.
- Open the editor. STAT → 1:Edit.
- Type the data into the L1 column, pressing ENTER after each value.
- Run the summary. STAT → right arrow to CALC → 1:1-Var Stats.
- Confirm the list. On the CE and newer models a setup screen appears; leave List as L1, leave FreqList blank, and select Calculate. On older models it runs straight away — press ENTER once more.
- Read the results. Scroll with the down arrow if needed.
Reading the output screen
| Shows | Means |
|---|---|
| x̄ | The mean |
| Σx | Sum of the values |
| Σx² | Sum of the squared values |
| Sx | Sample standard deviation (n − 1) |
| σx | Population standard deviation (n) |
| n | How many values it used |
| minX, Q1, Med, Q3, maxX | The five-number summary |
Sx or σx? Sx if your numbers are a sample of something larger — which is usually the case. σx only if they are the complete population. The distinction is explained here. The TI-84 shows both precisely because it cannot know which you meant.
Glance at n before writing anything down. If it does not match how many values you typed, the list had leftover data or you missed an entry.
Getting the variance, and the symbols it is not shown under
There is no variance on the 1-Var Stats screen, and no symbol for it anywhere on a TI-84. People hunt for σ² or s² and conclude the calculator cannot do it. It can — the variance is simply the standard deviation squared, so square whichever of the two the question wants:
- Sample variance (s²): run 1-Var Stats, then VARS → 5:Statistics → Sx, and press x² enter.
- Population variance (σ²): the same, choosing σx instead.
Pulling Sx from the VARS menu rather than retyping the digits you read off the screen matters more than it looks: the display is rounded, and squaring a rounded value compounds the error. The VARS route squares the full-precision number the calculator is actually holding.
The symbols themselves are worth keeping straight, because the TI labels differ from the ones in a textbook — the book's s is the calculator's Sx, and its σ is σx, where the trailing x is only the list's name. The notation guide compares the labels across TI, Casio, Sharp and HP, and the variance calculator will check whatever you get.
Data given as a frequency table
When the problem gives values with frequencies, enter the values in L1 and the frequencies in L2, then tell 1-Var Stats to use both.
- Enter the values in L1 and the matching counts in L2.
- STAT → CALC → 1:1-Var Stats.
-
On the CE, set List: L1 and FreqList: L2, then Calculate.
On older models, type
L1,L2after the command — 2nd 1, comma, 2nd 2 — then ENTER.
The reported n will now be the total frequency rather than the number of rows. The grouped data calculator does the same thing, and is a quick way to check the machine.
When it goes wrong
| Symptom | Cause | Fix |
|---|---|---|
| Answer close but not equal to the book's | Read σx instead of Sx, or vice versa | Check which the question wants |
| ERR: DIM MISMATCH | L1 and L2 have different lengths | Make the frequency list match |
| ERR: STAT | The list is empty, or has one value in sample mode | Re-enter the data |
| n is too large | Leftover values below your new data | ClrList and retype |
| L1 is missing from the editor | DEL pressed on the list header | STAT → 5:SetUpEditor → ENTER |
Other calculators, briefly
- TI-Nspire: add a Lists & Spreadsheet page, name a column, then menu → Statistics → Stat Calculations → One-Variable Statistics.
- TI-36X Pro: data to enter values, then 2nd data → 1-Var Stats → CALC.
- Casio fx-991EX: MENU → Statistics → 1 (1-Variable), enter data, then OPTN 3 (1-Variable Calc). Casio labels the two standard deviations σx and sx.
- Casio fx-83GT PLUS / fx-85GT PLUS: MODE 2 (STAT) 1 (1-VAR), enter data, AC, then SHIFT 1 (STAT) 4 (Var).
- Every other Casio, including the fx-991CW, fx-82MS and graphing models: the Casio guide has the full keystrokes.
Check the machine's answer
Separate numbers with commas, spaces or new lines, or paste a spreadsheet column.
Decimals and negatives are fine; write 10:3 for a value that occurs 3 times.
Your results will appear here: the standard deviation first, then the rest of the summary and a chart.
Standard deviation (sample)
3.04432
3.04
Your values typically sit about 3.04 above or below their mean of 15.88, in the same units as your data. 5 of 8 values (63%) fall between 12.83 and 18.92, within one standard deviation of the mean; for normally distributed data about 68% would.
Population SD (σ): 2.8477, if these values are the whole group.
- Count (n)
- 8
- Mean (x̄)
- 15.875
- Variance (s²)
- 9.26786
- Standard error
- 1.07633
- Minimum
- 12
- Q1 (25%)
- 13.75
- Median
- 15.5
- Q3 (75%)
- 17.5
- Maximum
- 21
- Range
- 9
More statistics (5)
- Relative SD (%RSD)
- 19.1768%
- Coefficient of variation
- 0.191768
- Sum (Σx)
- 127
- Sum of squares, Σ(x − x̄)²
- 64.875
- IQR (Q3 − Q1)
- 3.75
Data distribution
Shaded bands mark ±1, ±2 and ±3 SD from the mean. 5 of 8 values (63%) fall within ±1 SD.
Chart as text
Mean 15.875, sample standard deviation s = 3.04432, from 8 values between 12 and 21.
- Within ±1 SD (12.83 to 18.92): 5 of 8 values (63%). About 68% for normal data.
- Within ±2 SD: 8 (100%). About 95% for normal data.
- Within ±3 SD: 8 (100%). About 99.7% for normal data.
Show the working, step by step
Related calculators
-
Standard deviation calculator
Check the value your TI-84 gave you.
-
SD in Excel
The same calculation in a spreadsheet.
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SD on Casio
Keystrokes for fx-991EX, fx-83GT and every other Casio model.
-
Sx or σx?
Which of the two the TI-84 shows you to read.
-
Grouped data
The frequency-list version of the same idea.
Common questions
Which value on the TI-84 is the standard deviation?
Sx is the sample standard deviation (divides by n − 1). σx is the population standard deviation (divides by n). The calculator shows both; you choose which to read.
Most homework problems want Sx.
Why does my TI-84 give a different answer from the textbook?
Nearly always because you read σx where the book wanted Sx, or the reverse. Check that first — the two always differ, and by a lot on small datasets.
The second most common cause is leftover data in L1 from a previous problem. Clear the list before entering new values.
How do I clear a list on the TI-84?
Press STAT, choose 4:ClrList, then 2nd 1 to name L1, and press ENTER.
Alternatively, in the list editor put the cursor on the L1 header itself and press CLEAR then ENTER. Pressing DEL on the header removes the whole list, which is not what you want.
What is the difference between 1-Var Stats and 2-Var Stats?
1-Var Stats summarises a single list — mean, standard deviation, quartiles. 2-Var Stats works on paired data in two lists and adds the correlation and regression quantities. For a standard deviation you want 1-Var Stats.
Does this work on the TI-83 and TI-84 Plus CE?
Yes. The keystrokes are identical across the TI-83, TI-83 Plus, TI-84 Plus, TI-84 Plus Silver and TI-84 Plus CE. Only the screen colour differs.
How do I find standard deviation on a TI-84 Plus CE?
The steps are the same as on any TI-84 model. Enter your data into a list (usually L1), press STAT then CALC then 1-Var Stats, press ENTER twice, and scroll down to Sx for the sample standard deviation. The Plus CE has a colour screen but the menu layout is identical.
How do I find sd on TI-84?
"SD" on the TI-84 means the same as standard deviation. After entering your data and running 1-Var Stats, scroll down to Sx (sample SD, divides by n-1) or sigma x (population SD, divides by n). For most homework problems use Sx.
How do I find variance on TI-84?
The TI-84 shows variance indirectly. After running 1-Var Stats, read Sx (sample SD) or sigma x (population SD), then square it. For example, if Sx = 3.2, the sample variance is 3.2^2 = 10.24. The calculator does not display variance directly in the 1-Var Stats output.
Can I enter frequency data on a TI-84?
Yes. If your data has repeated values, put the unique values in L1 and the frequencies in L2, then run 1-Var Stats L1, L2 (note the comma and list name). The calculator will weight each value by its frequency. This is faster than typing every repeated value individually and avoids rounding errors.
Why does my TI-84 show both Sx and sigma x?
The TI-84 always computes both because it does not know whether your data is a complete population or a sample. Sx divides the sum of squared deviations by n - 1 (Bessel's correction). Sigma x divides by n. For the same data, Sx is always slightly larger. If your textbook or instructor says "sample," use Sx.