What Is Calculator With Standard Deviation?
Scientific and graphing calculators have a statistics mode that lists the one-variable statistics for a data list. This page gives you the same screen in your browser, with no keys to press.
Enter your values to get n, Σx, Σx², the mean, Sx (sample SD), σx (population SD) and the five-number summary. A table uses the same symbols as a handheld calculator, so you can check your own device.
Below are the formulas, a worked example and answers on Sx versus σx.
How to Use the Calculator With Standard Deviation Calculator
- Enter your list.
- Read the 1-Var Stats table.
- Pick Sx for a sample.
- Use the box plot to see the spread.
Calculator With Standard Deviation Formula
Sx
σx
Calculator With Standard Deviation Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x̄ | Mean | |
| Sx | Sample standard deviation | |
| σx | Population standard deviation | |
| Σx, Σx² | Sum and sum of squares |
Calculator With Standard Deviation Worked Example
For 4, 8, 6, 5, 3, 7, 9, 5, 6, 10 the sum is 63 and n = 10, so the mean is 6.3. The sum of squared deviations is 44.1, so Sx = √(44.1 ÷ 9) = 2.2136 and σx = √(44.1 ÷ 10) = 2.1.
With the example values loaded in the calculator above, the steps are:
- A scientific or graphing calculator’s one-variable statistics (1-Var Stats) screen lists these same values.
- x̄ = Σx ÷ n = 63 ÷ 10 = 6.3.
- Sx uses n − 1: √(44.1 ÷ 9) = 2.2135944.
- σx uses n: √(44.1 ÷ 10) = 2.1.
Result: Sample standard deviation Sx = 2.2135944; Population standard deviation σx = 2.1; Mean x̄ = 6.3.
How to Read One-Variable Statistics
The output matches the one-variable mode on a scientific calculator. For 4, 8, 6, 5, 3, 7, 9, 5, 6, 10 the sum is 63 and n = 10, so the mean is 6.3. Sx = 2.2136 is the sample standard deviation and σx = 2.1 is the population value.
Use Sx when the data are a sample. Σx and Σx² are the raw sums that the calculator uses internally, so you can check the arithmetic by hand with the shortcut formula.
Where Calculator With Standard Deviation Is Used
Matching your calculator
Compare the figures with the output of a scientific or graphing calculator.
Exam practice
Check Sx, σx, Σx and Σx² for a small data set.
Quartiles
See the five-number summary alongside the standard deviation.
Hand checks
Use Σx and Σx² to verify the shortcut formula.
Common Calculator With Standard Deviation Mistakes to Avoid
- Sx divides by n − 1 and σx divides by n. Choose the one that matches your data.
- Different calculators compute quartiles with different rules, so your device may differ slightly.
- Clear the previous data before you start on a handheld calculator. Old entries stay in memory.
- Check the count n first. A missing value changes every result.
Calculator With Standard Deviation Terms and Definitions
- 1-Var Stats
- The one-variable statistics command on graphing calculators.
Calculator With Standard Deviation FAQs
How do I find standard deviation on a calculator?
Put the calculator in one-variable statistics mode, enter the data, then read Sx or σx from the results. This page does the same and shows both.
What is the difference between Sx and σx?
Sx is the sample standard deviation, with n − 1 in the divisor. σx is the population standard deviation, with n in the divisor. For the example, Sx = 2.2136 and σx = 2.1.
What do Σx and Σx² mean?
Σx is the sum of the values and Σx² is the sum of their squares. With n they give the mean and standard deviation without listing each deviation.
Why might my calculator quartiles differ?
There are several accepted ways to compute quartiles, and calculators do not all use the same one. The values can differ by a small amount for the same data.