How to find a confidence interval for a mean on the Casio fx-CG50
t and z confidence intervals for a population mean, from a list of data or from summary statistics. 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
AI HL: confidence intervals for a mean, with the t-distribution when σ is unknown (the usual case) and the normal distribution when σ is known. Interpret the interval in context.
Practise it: HL AI confidence intervals and tests for means · HL AI CLT.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Confidence intervals 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, data in List 1.
- t-interval: F4 (INTR) F2 (t) F1 (1-SAMPLE). Data: List, C-Level 0.95, List: List1, Freq 1. Execute. Read Left and Right.
- z-interval (σ known): F4 (INTR) F1 (Z) F1 (1-SAMPLE), C-Level 0.95, σ 0.3, List1. Execute.
- From summary statistics: choose Data: Variable and type x̄, sx (or σ) and n instead of a list.
- C-Level is a decimal (0.95), not 95.
Confidence intervals 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.
- Data in L1. stat → TESTS → 8: TInterval. Inpt: Data, List L1, Freq 1, C-Level 0.95. Calculate.
- σ known: 7: ZInterval, σ 0.3.
- Summary statistics: Inpt: Stats and type x̄, Sx and n.
Confidence intervals 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.
- Data in a named list. menu → Statistics → Confidence Intervals → t Interval → Data. Choose the list, C Level 0.95. OK.
- σ known: z Interval.
- The results are stored as stat.CLower and stat.CUpper.
Worked example
Masses (kg): 4.2, 3.9, 4.5, 4.1, 3.8, 4.4, 4.0, 4.3, 3.7, 4.6. (a) Find a 95% confidence interval for the mean. (b) The same, if σ = 0.3 is known.
Answers (checked with Python)
x̄ = 4.15, s = 0.302765. (a) t-interval: (3.93341, 4.36659). (b) z-interval: (3.96406, 4.33594).
Common calculator mistakes
- Using a z-interval when σ is unknown and estimated from the sample (use t).
- Typing 95 instead of 0.95 for the level.
- Giving the interval without interpreting it: "we are 95% confident the population mean lies between 3.93 and 4.37 kg".
- Using σ where the question gives a sample standard deviation, or dividing by n instead of √n.
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 a list M of the data.
- tinterval(M) gives the t-interval; its menu sets the confidence level.
- Check by hand: mean(M) ± tdist(9).inversecdf(0.975) × stdev(M)/√10.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
M=[4.2,3.9,4.5,4.1,3.8,4.4,4,4.3,3.7,4.6]tinterval(M)mean(M)-tdist(9).inversecdf(0.975)·frac{stdev(M)}{√{10}}
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.