The TI-84 doesn’t display sample variance directly in its statistics output, but you can get it in about 30 seconds by running 1-Var Stats and then squaring the sample standard deviation. Here’s exactly how to do it, button by button.
Enter Your Data Into a List
Before you can calculate anything, your data needs to live in one of the calculator’s list columns (L1, L2, etc.).
- Press [STAT], then press [ENTER] (or press [1]) to select “Edit.”
- You’ll see columns labeled L1, L2, L3, and so on. Move your cursor to the first empty row in L1.
- Type each data value and press [ENTER] after each one. The values will stack in the column as you go.
- When you’ve entered all your data, press [2nd] then [QUIT] to return to the home screen.
If L1 already has old data in it, clear it first: from the Edit screen, highlight the L1 header at the top of the column, press [CLEAR], then [ENTER].
Run 1-Var Stats
Press [STAT], then scroll right to the CALC menu. Press [ENTER] or [1] to select “1-Var Stats.” On newer TI-84 models, a setup screen appears. Make sure “List” is set to L1 and “FreqList” is blank (unless you’re using a frequency column). Arrow down to “Calculate” and press [ENTER].
On older OS versions, the calculator may paste “1-Var Stats” directly to the home screen. If that happens, just press [ENTER] and it will default to L1.
The calculator now shows a list of summary statistics: the mean (x̄), the sum of all values (Σx), and two standard deviations labeled Sx and σx. You may need to scroll down to see all the output.
Know Which Symbol to Use
This is the step most people get wrong. The TI-84 gives you two standard deviations, and picking the wrong one will give you the wrong variance.
- Sx is the sample standard deviation. It divides by n minus 1. This is the one you want for sample variance.
- σx is the population standard deviation. It divides by n. Use this only when your data set represents the entire population, not a sample drawn from a larger group.
In most statistics courses, you’re working with samples, so Sx is almost always the correct choice.
Square Sx to Get Sample Variance
Variance is just the standard deviation squared. You could read the Sx value off the screen, retype it, and square it, but that introduces rounding errors. Instead, pull the stored Sx variable directly from the calculator’s memory so you square the full-precision value.
From the home screen:
- Press [VARS].
- Press [5] to select “Statistics.”
- Press [4] to paste “Sx” onto the home screen.
- Press [x²] (the squaring key, located on the left side of the keypad).
- Press [ENTER].
The number on screen is your sample variance, calculated with zero rounding error. If you need population variance instead, repeat this process but choose σx (option 5 in the same Statistics menu) and square that.
Quick Summary of the Full Sequence
Once you’ve done this a few times, the whole process takes under a minute:
- Enter data: [STAT] → [ENTER] → type values into L1 → [2nd][QUIT]
- Run stats: [STAT] → right arrow to CALC → [ENTER] → set List to L1 → Calculate → [ENTER]
- Get variance: [VARS] → [5] → [4] → [x²] → [ENTER]
Using Frequency Data
If your data is organized as a frequency distribution (one column for values, another for how often each value appears), enter the values in L1 and the frequencies in L2. When you set up 1-Var Stats, change the “FreqList” field to L2. The calculator will weight each value by its frequency, and the resulting Sx will reflect that. Square it the same way to get variance.
Why the TI-84 Doesn’t Show Variance Directly
The 1-Var Stats output includes the mean, standard deviation, min, max, median, and quartiles, but not variance. Texas Instruments designed the output around the most commonly referenced statistics. Since variance is simply the standard deviation squared, the extra step of squaring Sx through the VARS menu is the intended workflow. There’s no hidden variance function buried in another menu that would save you a step.