How to find the mean, standard deviation and quartiles (1-var and 2-var statistics) on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
On the fx-CG50: MENU → 2 (STATISTICS) … F1 (1-VAR).On the TI-84 Plus CE: stat → CALC → 1: 1-Var Stats.On the TI-Nspire CX II: menu → Statistics → Stat Calculations → One-Variable Statistics.
Mean, standard deviation, quartiles and sums from a list or a frequency table. 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
Descriptive statistics in every course: the mean and standard deviation of a frequency table, the five-number summary for a box plot, and outliers (1.5 × IQR). The IB's "standard deviation" is σ (divide by n).
Practise it: SL AI descriptive statistics · SL AA measures of central tendency · SL AA presentation of data.
Which IB course and paper
| Course | GDC papers | What you use it for |
|---|---|---|
| AA SL | Paper 2 (Paper 1 is calculator-free) | Mean, standard deviation, quartiles and outliers from a list or frequency table. |
| AA HL | Papers 2 and 3 (Paper 1 is calculator-free) | As SL. |
| AI SL | Papers 1 and 2 | As AA SL. |
| AI HL | Papers 1, 2 and 3 | As SL. |
A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.
Topic notes: Mean, median, mode, and IQR (AA SL).
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
1-variable and 2-variable statistics 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).
Watch the key presses on the fx-CG5011 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- MENU 2 (STATISTICS). Values in List 1, frequencies in List 2.
- F2 (CALC) F6 (SET): 1Var XList = List1, 1Var Freq = List2. EXIT.
- F1 (1-VAR). Read x̄, σx, sx and n; scroll down with ▼ for minX, Q1, Med, Q3, maxX and Mod.
- Two variables: put y in List 2 (frequency back to 1), then F2 (2-VAR) for x̄, ȳ, Σxy and so on.
- Grouped data: type the class midpoints as the values.
- Box plot: F1 (GRAPH) F6 (SET), Graph Type: MedBox, then F1 to draw. Outliers are shown if you choose Outliers: On.
- fx-CG50 OS 3.x has a setting for how Q1 and Q3 are worked out (in SET UP). Leave it on the standard setting: it matches the IB and exam-board method (medians of the lower and upper halves).
1-variable and 2-variable statistics 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.
Watch the key presses on the TI-84 Plus CE10 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- stat 1: Edit. Values in L1, frequencies in L2.
- stat → CALC → 1: 1-Var Stats. List: L1, FreqList: L2. Calculate.
- Scroll down for n, minX, Q1, Med, Q3, maxX. σx is the population standard deviation; Sx the sample one.
- Two variables: 2: 2-Var Stats with Xlist L1, Ylist L2.
- Frequencies must be whole numbers for the quartiles to be given.
1-variable and 2-variable statistics on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS (the CX II CAS is a different model: check the exam rules before using one).
- Lists & Spreadsheet: values in column A (name it x), frequencies in column B (name it f).
- menu → Statistics → Stat Calculations → One-Variable Statistics, Num of Lists 1, OK.
- X1 List: x, Frequency List: f, OK. Read x̄, σx, sx, n, MinX, Q1X, MedianX, Q3X, MaxX.
For teachers: Show on the board Print a keystroke card Teaching GDC skills
Worked example
Scores 2, 3, 4, 5, 6 with frequencies 3, 7, 8, 5, 2. Find n, the mean, the standard deviation and the quartiles.
Answers (checked with Python)
n = 25, x̄ = 3.84, σ = 1.12 (sample s = 1.14310), Q1 = 3, median = 4, Q3 = 5.
Now try it on an exam-style question
Use the keystrokes above on IB-style descriptive statistics questions. Free to try, no sign-up.
Common calculator mistakes
- Forgetting the frequency list: with 1Var Freq = 1 the calculator treats the table as five single values.
- σ vs s: IB and most exam questions want σx (divide by n). s (sx) is the unbiased estimate, only when asked.
- Old data or an old frequency setting left from the last question.
- Using class boundaries instead of midpoints for grouped data.
- Estimates: from grouped data the mean and standard deviation are estimates; say so.
- Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).
If you get an error
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:DIM MISMATCH, ERR:INVALID DIM, ERR:SYNTAX, ERR:STAT
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:DIM MISMATCH Lists or matrices in the same operation have different sizes (TI's example: multiplying two lists with different numbers of elements). Check: L1 and L2 with different numbers of values (one value missed or typed twice), a frequency list of the wrong length, or matrices whose sizes cannot be multiplied. Fix: Make the lists the same length, or check the size of each matrix.
ERR:INVALID DIM TI's knowledge base: one or more stat plots are turned on, but the lists they use are empty. Check: A stat plot left on from a statistics question, so the error appears when you graph a function. Fix: Turn off the stat plots you are not using, or put the data back in the lists.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
ERR:STAT A statistics calculation was tried on lists that are not suitable. A statistical analysis needs at least two data points. Check: An empty or one-value list, or the wrong list named in the command. Fix: Check the lists named in the command and the data in them.
TI-Nspire CX II: Domain error, Dimension mismatch, Syntax error
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Dimension mismatch Two or more arguments must have the same dimension and do not (TI's example: [1,2]+[1,2,3]). Check: Lists of different lengths in a statistics command, or vectors or matrices of different sizes. Fix: Make the lists, vectors or matrices the sizes the operation needs.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
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).
- Type the data as one list, each value as many times as its frequency: D = [2, 2, 2, 3, 3, …].
- mean(D), stdevp(D) (σ, divide by n), stdev(D) (s, divide by n − 1), quartile(D, 1), median(D), quartile(D, 3).
- Desmos's quartile() may use a different rule from your GDC for some data sets: in the exam the GDC's (medians of the halves) is the one to use.
Open desmos.com/calculator (free, in any browser) and type:
D=[2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6]mean(D)stdevp(D)stdev(D)quartile(D,1)median(D)quartile(D,3)boxplot(D)
Questions
Can I use a calculator for 1-variable and 2-variable statistics in the exam?
In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well.
What are the fx-CG50 keystrokes for 1-variable and 2-variable statistics?
MENU 2 (STATISTICS). Values in List 1, frequencies in List 2. Then F2 (CALC) F6 (SET): 1Var XList = List1, 1Var Freq = List2. EXIT. Then F1 (1-VAR). Read x̄, σx, sx and n; scroll down with ▼ for minX, Q1, Med, Q3, maxX and Mod. The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.
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 models 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. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.