Standard Deviation on a TI-84 Calculator: Find Sx and σx

Quick Answer

On a TI-84 calculator, enter your data in a list, run `1-Var Stats`, and then read the standard deviation from the results screen. The calculator shows `Sx` for the sample standard deviation and `σx` for the population standard deviation.

That means the button sequence is usually: `STAT` → `EDIT` to enter values, then `STAT` → `CALC` → `1:1-Var Stats` to calculate the summary. If you want to verify the answer outside the handheld, compare it with the site's sample standard deviation calculator, population standard deviation calculator, or mean calculator.

Step-by-Step TI-84 Workflow

The arithmetic is automatic on the TI-84. Most wrong answers come from stale list data, picking the wrong list, or reading `σx` when the assignment expects `Sx`.

STAT -> 1:Edit
Enter data in L1
STAT -> CALC -> 1:1-Var Stats
List: L1
Calculate

Sx vs σx on the TI-84

This is the part that confuses most students. The TI-84 gives you both versions of standard deviation on the same results screen because the calculator does not know whether your list is a sample or a full population.

Worked Example: Quiz Scores

Suppose your TI-84 list `L1` contains eight quiz scores: `72, 75, 81, 79, 68, 74, 77, 84`. If those scores come from one section of a larger course, the section is a sample, so `Sx` is the number to report.

L1 = {72, 75, 81, 79, 68, 74, 77, 84}
STAT -> CALC -> 1:1-Var Stats
List: L1
Calculate

For this list, the mean `x̄` is 76.25, the sample standard deviation `Sx` is about 5.25, and the population standard deviation `σx` is about 4.91. The numbers differ because the sample version uses the same `n - 1` logic explained in Bessel Correction (n-1) Explained.

After you have the spread, a common next step is standardizing one score. Use the z-score calculator or read Z-Score Explained if you need to turn one student's score into a relative position.

Using a Frequency List

If values repeat many times, the TI-84 can summarize them more efficiently with a data list and a frequency list. That is useful when a teacher gives a short table like score 2 appears 3 times, score 4 appears 5 times, score 6 appears 2 times.

Common TI-84 Mistakes

• Reading `σx` when the assignment asks for a sample:This is the most common exam mistake because both outputs appear together on the TI-84 results screen.
• Leaving old values in the list:If `L1` already contains hidden leftovers from a previous problem, `n`, the mean, and both standard deviations will all be wrong.
• Entering frequencies as raw data:A list like `3, 5, 2, 2` only belongs in `L2` when it represents counts. It is not the same as entering the repeated observations themselves.
• Mixing units in one list:Seconds and milliseconds, dollars and cents, or percentages and counts cannot be combined meaningfully in one standard deviation calculation.

If your result looks strange, first check `n`, then inspect the list entries, and then confirm whether you should be reporting `Sx` or `σx`. For a broader cross-check, the site's descriptive statistics calculator and variance calculator are the fastest sanity checks.

TI-84 Checklist

The core TI-84 workflow is simple once the statistical choice is clear: enter data, run `1-Var Stats`, and report `Sx` or `σx` based on whether the list is a sample or a full population.