Find the standard deviation

Measure how spread out a list is, using the sample or the population formula.

Standard deviation says how far values typically sit from the mean. A small number means the data is tightly bunched; a large one means it is spread out.

Use the sample standard deviation (s, written Sx or sx) when your data is a sample of a bigger group. Use the population one (σ) when you have the whole group.

The example list is 2, 4, 6, 8, 10: s is about 3.1623 and σ is about 2.8284.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

Type the numbers into L1.
stat12enter4enter6enter8enter10enter
Run 1-Var Stats from STAT, CALC, option 1. Move down to Calculate and press enter.
stat▶1▼▼enter

You should seeSx is the sample value and σx is the population value.

Classic Graphing 84 key reference · Classic Graphing 84 manual

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

Open Statistics, choose 1-Variable and type the numbers.
MENU612=4=6=8=10=AC
Press OPTN and choose 1-Variable Calc. Then press the down arrow twice to bring σx into view.
OPTN3▼▼

You should seeσx=2.828427125

Keep pressing the down arrow to find sx, the sample value, 3.162277660.

Natural Scientific 991 key reference · Natural Scientific 991 manual

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

Open the Statistics part of the menu and choose stDevSamp(.
menu63
Type the list in curly braces, close the bracket and press ctrl with enter for a decimal answer.
shift{(2,4,6,8,10shift}))ctrl≈enter

You should see3.16228

Use stDevPop( (menu, Statistics, option 4) for the population value. Plain enter gives an exact form such as √10.

Classic CAS key reference · Classic CAS manual

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

Clear the statistics memory first, so old data cannot sneak into the answer.
fCLR ΣGSB
Key in each number and press Σ+.
2Σ+4Σ+6Σ+8Σ+10Σ+
Press g then the decimal point key for the sample standard deviation s.
gs.

You should see3.1623

RPN Scientific 15 key reference · RPN Scientific 15 manual

RPN Financial 12

Start on the main screen: There is no menu to leave: the display always shows the X register. Press f then R/S (P/R) to leave program mode, and clear a pending prefix by pressing ON.

Clear the statistics registers with f then CLx.
fREGCLx
Key in each number and press Σ+.
2Σ+4Σ+6Σ+8Σ+10Σ+
Press g then the decimal point key for the sample standard deviation s.
gs.

You should see3.16

RPN Financial 12 key reference · RPN Financial 12 manual

Tips

The sample value is always a little bigger than the population value for the same data.
To turn s into σ by hand, multiply by the square root of (n - 1) divided by n.