To find standard deviation on a TI-84, enter your data in L1 with STAT, Edit, then run STAT, CALC, 1-Var Stats. Read Sx for a sample and σx for a whole population. Sx divides by n − 1 instead of n, so it is always a little larger than σx for the same data.
How to find standard deviation on a TI-84
These steps work on the TI-84 Plus, the TI-84 Plus CE, and the free TI-84 calculator online on our homepage. They are part of the same STAT menu covered in the TI-84 statistics calculators guide.
- Press STAT, then press 1 to open Edit.
- If L1 already holds numbers, press the up arrow to highlight the L1 heading, then press CLEAR and ENTER.
- Type each value and press ENTER after it.
- Press 2nd, then MODE to quit to the home screen.
- Press STAT, press the right arrow to highlight CALC, and press 1 for 1-Var Stats.
- If a screen asks for a list, set List to L1, leave FreqList blank, and select Calculate.
- Read Sx and σx. Press the down arrow to scroll to the values below them.
Older TI-84 Plus models skip the list screen in step 6 and paste 1-Var Stats onto the home screen. Press ENTER there and the calculator uses L1 on its own.
Worked example with 8 data points
Say eight students scored 2, 4, 4, 4, 5, 5, 7, and 9 on a 10 point quiz. Enter those values in L1 and run 1-Var Stats. The calculator shows these numbers.
| Symbol | What it means | Value |
|---|---|---|
| x̄ | Mean of the data | 5 |
| Σx | Sum of the values | 40 |
| Σx² | Sum of the squared values | 232 |
| Sx | Sample standard deviation | 2.138089935 |
| σx | Population standard deviation | 2 |
| n | Number of values | 8 |
You can check this by hand. Subtract the mean of 5 from each score and square the result. That gives 9, 1, 1, 1, 0, 0, 4, and 16, which add up to 32.
Divide 32 by n, which is 8, and you get 4. The square root of 4 is 2, which matches σx. Divide 32 by n − 1, which is 7, and you get 4.571428571. Its square root is 2.138089935, which matches Sx.
Sx vs σx explained
Sx is the sample standard deviation and σx is the population standard deviation. The only difference in the formulas is the number you divide by.
- Sx = √(Σ(x − x̄)² ÷ (n − 1))
- σx = √(Σ(x − x̄)² ÷ n)
Use Sx when your numbers are a sample taken from a bigger group. Surveying 40 students to learn about a school of 1,200 is a sample. Most homework and almost every AP Statistics problem uses Sx, which your textbook may write as s.
Use σx when you have every member of the group you care about. The heights of all 12 players on one basketball team, and nobody else, form a population.
Why divide by n − 1? A sample usually misses the most extreme values in the full group, so its spread comes out a bit small. Dividing by a smaller number pushes the answer back up to a fairer estimate.
Once you have a standard deviation, you can measure how far one value sits from the mean with the z-score calculator.
Why your answer is wrong: old list data
The most common reason a TI-84 gives the wrong standard deviation is old numbers left in L1. If last week's data had 12 values and today's has 8, the last 4 old values stay in the list and get counted.
Always look at the n value on the 1-Var Stats screen. If n does not match how many numbers you typed, the list has extra data. Clear it with STAT, 4:ClrList, then 2nd 1 for L1, and ENTER. Then type your data again.
The second cause is a frequency list. If FreqList is set to L2 and L2 holds old numbers, each value gets counted the wrong number of times. Leave FreqList blank unless your problem gives you frequencies. To empty every list at once before a new unit, use a RAM reset.
Common mistakes
- Reporting σx when the problem describes a sample. If the data came from part of a larger group, give Sx.
- Typing a negative value with the subtraction key. Use the (−) key, or the TI-84 shows ERR:SYNTAX, one of the TI-84 error codes students see most.
- Rounding the mean before working by hand. Keep every digit until the last step, or your answer drifts.
- Squaring Sx and calling it the standard deviation. Sx squared is the sample variance, a different number.
FAQ
What is the difference between Sx and sigma x on a TI-84?
Sx is the sample standard deviation and divides by n − 1. Sigma x, written σx, is the population standard deviation and divides by n. For the same data, Sx is always slightly larger. The gap shrinks as n grows, so with 100 values the two are almost equal.
Which standard deviation do I use on a TI-84?
Use Sx unless the problem says your data is the entire population. Samples are far more common in class, and AP Statistics uses Sx almost every time. Pick σx only when you measured every member of the group, such as all students in one small class.
How do I clear a list on a TI-84?
Press STAT, then 4 for ClrList, then 2nd 1 to paste L1, and press ENTER. The screen shows Done. You can also open STAT, Edit, move the cursor up onto the L1 heading, and press CLEAR then ENTER. Avoid DEL on the heading, which removes the list from the editor.
Why is my standard deviation wrong on the TI-84?
The usual cause is old data left in L1, which shows up as an n value larger than your count. Other causes are a FreqList set to an old list, running 1-Var Stats on the wrong list, or reading σx when the problem wants Sx. Check n first.
How do you find variance on a TI-84?
Square the standard deviation. After 1-Var Stats, press VARS, 5 for Statistics, 3 for Sx, then the x² key and ENTER. That gives sample variance. You can also press 2nd STAT, move right to MATH, and choose 8 for variance(, then type L1 and close the parenthesis.
Where is 1-Var Stats on a TI-84?
Press STAT, then press the right arrow once to reach the CALC menu. 1-Var Stats is the first item, so press 1 or ENTER. On a TI-84 Plus CE a short screen asks which list to use. Choose L1 and select Calculate to see the results.