How to Find Standard Deviation on a TI-84 (Plus and CE)

The standard deviation tells you how tightly a set of values clusters around its own mean, and the TI-84 Plus and TI-84 Plus CE give you two of them from a single command. Press STAT ▸ CALC ▸ 1:1-Var Stats and the screen returns the mean, the count and both a sample and a population standard deviation. Learning how to find standard deviation on a TI-84 is therefore less about the keystrokes and more about choosing the right output line.

That choice is where marks are lost. Sx and σx are different numbers computed in slightly different ways, and writing the wrong one turns a correct calculation into a wrong answer. This page walks through the whole procedure with a five-value data set, shows the arithmetic behind each figure, and explains which one your teacher is expecting.

Enter the data in L1

Press STAT, choose 1:Edit and press ENTER. The editor opens with six columns, L1 to L6, and the cursor in the first cell of L1. Type the first value and press ENTER to move down; repeat until every value is in the column. The arrow keys let you move back to fix a mistake without retyping the whole list.

If L1 already contains numbers from an earlier question, empty it first: move the cursor onto the L1 heading at the top and press CLEAR then ENTER. Starting from a stale list is the most common reason a standard deviation comes out looking wrong.

Run 1-Var Stats

With the data in place, press STAT again, move the cursor right to the CALC menu, and select 1:1-Var Stats. Pressing ENTER pastes the command onto the home screen as 1-Var Stats; pressing ENTER once more runs it. By default it reads L1, which is what you want.

If you are using a frequency table, type the list name after the command and set the FreqList field to the matching frequency list before you run it.

What the 1-Var Stats screen is telling you

The output is a list of values, and each line has a specific job.

• x̄ is the arithmetic mean.
• Σx is the sum of the values and Σx² is the sum of their squares; both feed the variance.
• Sx is the sample standard deviation.
• σx is the population standard deviation.
• n is how many values were used.

Press the down arrow and the screen continues with minX, Q1, Med, Q3 and maxX — the five-number summary you need for a box plot.

Sx or σx: which one does your teacher want

Both numbers describe spread, but they answer slightly different questions. Sx treats the list as a sample taken from a larger group and divides the summed squared deviations by n − 1. σx treats the list as the entire population and divides by n. Because n − 1 is smaller than n, Sx is always the larger of the two — never assume the two are interchangeable.

The convention in AP Statistics is that sample data uses Sx and s, while population data uses σx and σ. If a question says “a random sample of thirty students”, you want Sx. If it says “the population of all values”, you want σx.

A worked example with five values

Take the values 5, 7, 8, 9 and 11. They sum to 40, so the mean is 8.

The squared deviations total 20. Dividing by n − 1, which is 4, gives a sample variance of 5, and its square root is 2.236067978 — the Sx on the screen. Dividing the same 20 by n, which is 5, gives a population variance of exactly 4, and its square root is 2 — the σx on the screen. The two answers differ only because of the number you divide by, which is why the choice matters.

In a real statistics answer you would quote these to two or three decimal places, so Sx ≈ 2.236 and σx = 2.

When the numbers look wrong

If 1-Var Stats refuses to run and shows ERR: INVALID DIM, the list it was pointed at is almost certainly empty. See the ERR: INVALID DIM fix for the full check. A standard deviation that comes out far too large is usually caused by a stray value left in the list, or by mixing up which list the command used.

For two-list statistics the lists must be the same length; if they are not, the calculator raises ERR: DIM MISMATCH instead. That error is described on the ERR: DIM MISMATCH page, and it matters because a single mismatched pair of lists can invalidate the whole summary.

On the AP exams that permit a graphing calculator, the TI-84 Plus and Plus CE are allowed, but AP Calculus bans a calculator with a computer algebra system. The rules are revised from time to time, so confirm the current wording with the AP calculator policy and with your teacher before the exam. When your data is two-variable, use the method on our linear regression tutorial; when you need the median and the mode as well, see mean, median and mode.