Summarise paired data (x and y)

Get the means, spreads and cross-product sum for two lists of numbers that go together.

Two-variable statistics are for pairs, such as hours studied (x) and test score (y). The calculator summarises each list and also the products x times y.

The example pairs are x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5. The means are 3 and 4, and the sum of products is 66.

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 x values in L1 and the y values in L2.
stat11enter2enter3enter4enter5enter▶2enter4enter5enter4enter5enter
From STAT, move to CALC and pick 2-Var Stats.
stat▶2
The lists are L1 and L2 already. Move down to Calculate and press enter.
▼▼▼enter

You should seeScroll down to find ȳ, Sy, σy and Σxy.

Classic Graphing 84 key reference

Classic Scientific 30

Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.

Type the x values in L1 and the y values in L2.
data1enter2enter3enter4enter5enter▶▲▲▲▲▲2enter4enter5enter4enter5enter
Open the STAT menu with 2nd then data and choose 2-Var Stats. Accept the lists with enter.
2ndstatdata2enterenterenter

You should see2-Var 1:n=5 2:x̄=3 3:Sx=1.58113883

Classic Scientific 30 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

Type x into List 1 and y into List 2.
MENU21EXE2EXE3EXE4EXE5EXE▲▲▲▲▲▶2EXE4EXE5EXE4EXE5EXE
Choose CALC (F2), then 2-VAR (F2).
F2F2

You should seeScroll down to see ȳ, Σy, Σxy and the rest.

Natural Color Graphing key reference

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
For each pair, key in y, press ENTER, key in x, then press Σ+.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+4ENTER4Σ+5ENTER5Σ+
Press g then 0. The mean of x lands in X and the mean of y in Y.
gx̄0

You should see3.0000 4.0000

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

For each pair, key in y, press ENTER, key in x, then press the Σ+ key.
2ENTER1Σ+4ENTER2Σ+5ENTER3Σ+4ENTER4Σ+5ENTER5Σ+
Open the STAT menu with shift then ÷, and press the x̄ menu key. The mean of x, 3, appears.
⇧STAT÷√x
Press x<>y to bring the mean of y into view.
x⇄y

You should seeThe mean of x is 3 and the mean of y is 4; x<>y swaps which one is on the X line.

RPN Advanced 42 key reference

Tips

x goes first on graphing calculators (list 1 = x, list 2 = y). On RPN models x is in the X register and y in the Y register when you press Σ+.