How to find the mean, standard deviation and quartiles (1-var and 2-var statistics) on the Casio fx-CG50
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
Mean and standard deviation from raw data or a frequency table (the large data set), and the coded-data questions. Most A Level boards use σ (divide by n) unless they ask for an unbiased estimate s² (divide by n − 1).
Practise it: Statistical sampling and data · IAL S1.
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).
- 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.
- 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 not allowed in IB, A Level or IGCSE exams.
- 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.
1-variable and 2-variable statistics on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- Frequency column on: SHIFT MENU (SETUP) → ▼ → Statistics → Frequency? → On.
- MENU 6 1 (1-Variable). Type the values in x and the frequencies in Freq.
- OPTN → 1-Variable Calc. Scroll with ▼ for x̄, σx, sx, n, min, Q1, Med, Q3, max.
1-variable and 2-variable statistics 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 → 1-Variable.
- For a frequency table turn on the Freq column: TOOLS → Frequency → On.
- Type the data, then OK → 1-Var Results. Page down for Q1, Med, Q3, min and max.
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.
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.
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.
- 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.
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator 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)
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.