How to find Pearson's r and Spearman's rank correlation on the Casio fx-CG50
Pearson's product-moment correlation coefficient and Spearman's rank coefficient (by ranking, then r). Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
The product-moment correlation coefficient (PMCC) and its hypothesis test in A Level statistics; Spearman's rank in some Further Statistics options and IAL S3. Both come from the same regression screen.
Practise it: Hypothesis testing · Statistical sampling and data.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Correlation r and Spearman's rank on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 2 (STATISTICS). Type the x values into List 1 and the y values into List 2, pressing EXE after each. (Clear an old list first: highlight the list, F6 (▷) F4 (DELETE-ALL) F1 (Yes).)
- Pearson's r: F2 (CALC) F3 (REG) F1 (X) F1 (ax+b). Read r.
- Spearman: type the ranks of x into List 3 and the ranks of y into List 4 (rank each list separately, smallest = 1; tied values share the mean rank).
- F2 (CALC) F6 (SET): XList = List3, YList = List4, EXIT, then F3 (REG) F1 F1 again. This r is rs.
- Sorting helps you rank: F1 (TOOL) → SORT-ASC in the list editor, but sort a copy, not your original lists, or the x–y pairs break.
- Set the SET menu back to List1/List2 afterwards.
Correlation r and Spearman's rank on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- stat 1: Edit. Clear old data: move onto the L1 heading, clear, enter. Type the x values in L1 and the y values in L2.
- Diagnostics on (mode → STAT DIAGNOSTICS: ON), then stat → CALC → 4: LinReg(ax+b) with L1, L2. Read r.
- Spearman: type the ranks in L3 and L4 and run LinReg(ax+b) with Xlist L3, Ylist L4. That r is rs.
- No r on screen means diagnostics are off.
Correlation r and Spearman's rank on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Add a Lists & Spreadsheet page (ctrl doc → Add Lists & Spreadsheet). Name column A xs and column B ys in the top row, then type the data.
- menu → Statistics → Stat Calculations → Linear Regression (mx+b) with xs, ys. Read r.
- Spearman: add rank columns (rx, ry) and run the same regression on them.
Correlation r and Spearman's rank on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 6 2 (y = a + bx). Enter the x and y data.
- OPTN → Regression Calc: read r.
- Spearman: replace the data with the ranks (or start a new table of ranks) and read r again.
Correlation r and Spearman's rank on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Statistics → y = a + bx. Enter the data.
- OK → Regression Results: read r.
- Spearman: enter the ranks instead and read r.
Worked example
x: 12, 15, 17, 20, 23, 25, 28, 30. y: 40, 44, 43, 52, 55, 51, 60, 63. Find r and Spearman's rs.
Answers (checked with Python)
r = 0.955492. Ranks of x: 1–8; ranks of y: 1, 3, 2, 5, 6, 4, 7, 8. r of the ranks gives rs = 0.905.
Common calculator mistakes
- Ranking the two lists together instead of separately.
- Ties: two equal values in 3rd and 4th place both get rank 3.5, and the next value gets 5.
- Reordering one list only (sorting x without its y) destroys the pairs.
- Reading r² as r: r = 0.955 but r² = 0.913.
- Interpreting: r close to 1 means a strong positive linear relationship, not that x causes y.
Do it in Desmos
Not in the exam. Desmos is not allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- Make lists X = [12, 15, …] and Y = [40, 44, …].
- corr(X, Y) gives Pearson's r; spearman(X, Y) gives Spearman's rs directly (Desmos ranks and handles ties for you).
- Plot (X, Y) to see the scatter diagram.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
X=[12,15,17,20,23,25,28,30]Y=[40,44,43,52,55,51,60,63](X,Y)corr(X,Y)spearman(X,Y)
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.