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
Pearson's r in AA and AI; Spearman's rs in AI (SL and HL) when the relationship is monotonic but not linear, or the data are ranks. No GDC has a Spearman button: rank the data, then find r of the ranks.
Practise it: SL AI bivariate data · SL AI correlation and regression · SL AA bivariate 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.
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 an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- 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.
- 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.