Casio fx-CG50 lesson 10: Statistics: lists, 1-VAR, 2-VAR and regression

Statistics questions are where the fx-CG50 saves the most time, and where one wrong setting (an old list, the frequency left at 1, σx mixed up with sx) costs the most marks. This lesson builds one routine for every data question.

• Lesson 10 of 12
• About 55 minutes
• Casio fx-CG50 (OS 3)
• Free, no sign-in

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Which courses this lesson suits

• IB Maths AA (SL and HL): Papers 2 and 3
• IB Maths AI (SL and HL): every paper
• A Level Maths (UK and IAL): calculator allowed in every paper

Spearman's rank (AI) uses the same regression steps on the ranks: see the correlation guide below.

Before you start

Ask students to open STATISTICS (MENU 2) and look for data left in the lists from earlier work: old data in List 2 is the most common reason for a wrong mean.

The key presses, step by step

Every key is shown as it is printed on the calculator, like SHIFT or F1. The F-keys do whatever the bottom row of the screen says, so the picture next to each step shows that row.

1. MENU 2 (STATISTICS). To clear an old list, move the cursor onto it, then F6 (▷) F4 (DEL-ALL) F1 (Yes).

   Type the values 1, 2, 3, 4, 5 into List 1 and the frequencies 3, 7, 9, 4, 2 into List 2, with EXE after each number.

   Clear the lists first, every time. A leftover value at the bottom of a list is easy to miss and changes every answer.

   

2. F2 (CALC) F6 (SET). Set 1Var XList to List1 and 1Var Freq to List2 (with Freq highlighted, the F-keys offer 1 or List). Press EXIT.

   With the frequency left at 1 the calculator treats the frequencies as more data. This is the setting to check.

   

3. F1 (1-VAR). The first screen shows x̄ = 2.8, σx = 1.095445115, sx = 1.118033989 and n = 25. Scroll down with ▼ for minX, Q1, Med, Q3 and maxX: here Q1 = 2, Med = 3, Q3 = 3.5.

   σx divides by n (the data are the whole population); sx divides by n − 1 (an estimate from a sample). IB questions usually want σx unless they talk about estimating from a sample.

   

4. Two variables: clear the lists, then type x = 2, 3, 5, 6, 8, 9 (hours of revision) into List 1 and y = 52, 55, 63, 66, 74, 79 (test score) into List 2.

   F2 (CALC) F6 (SET): 2Var XList = List1, 2Var YList = List2, 2Var Freq = 1. EXIT.

   Check n on the results screen: it should equal the number of pairs, 6 here.

   

5. F2 (CALC) F3 (REG) F1 (X) F1 (ax+b). Read a = 3.826666667, b = 43.78666667 and r = 0.9984496302.

   Other models are in the same REG menu: F3 (X²) quadratic, F4 (X³) cubic, and after F6 (▷) log, exponential, power, sine and logistic.

   r is shown with the line. The logarithmic, exponential and power models also show r and r². The quadratic, cubic and quartic models show R² instead, and the sine and logistic models show neither.

   

6. To predict, keep every digit of a and b. In RUN-MATRIX type 7, then OPTN F5 (STAT) F2 (ŷ) EXE: ŷ at x = 7 is 70.57333333. Or type the line yourself with the full a and b from the screen.

   Back in STATISTICS, F5 (COPY) on the regression screen puts the line into the GRAPH list, and F6 (DRAW) draws it over the scatter diagram.

   The calculator uses the line from the last regression you ran, so run the regression for these data first.

   

Your turn: check your understanding

Try these straight after the key presses, on your own calculator, before looking at the answers.

1. Find the mean, σx and sx of 4, 7, 7, 9, 13. Which one would you give for "the standard deviation of these five values"?
2. For x = 1, 2, 3, 4 and y = 2, 5, 7, 10, find the regression line y = ax + b and r.

Exam efficiency

• One routine for every data question: clear the lists, type the data, check SET, then CALC.
• Check n on the results screen against the question before you copy anything down.
• Write the regression line with a and b to 3 s.f. (y = 3.83x + 43.8) but predict with the full values.
• A prediction inside the range of the x data (interpolation) with r close to ±1 is reliable; outside the range (extrapolation) it is not.
• Grouped data: type the class midpoints as the values and the frequencies in the next list.

Worked exam-style example

Practice

Do these on your own calculator. Write the answers to 3 significant figures unless the task says otherwise.

1. Find the mean, the standard deviation σx and the median of 12, 15, 9, 20, 14, 17, 11.
2. The values 10, 20, 30, 40 have frequencies 4, 6, 8, 2. Find the mean and σx. (Use a frequency list.)
3. For x = 1, 2, 3, 4, 5 and y = 3.1, 4.9, 7.2, 8.8, 11.1, find the regression line of y on x and r.
4. Use your line from task 3 to estimate y when x = 6.5. Is the estimate reliable?
5. Find Q1, the median and Q3 of 3, 5, 7, 8, 10, 12, 15, 20, and the interquartile range.

Common mistakes

• Old data left in a list: clear both lists first and check n.
• 1Var Freq left at 1 when the data come with frequencies, or left at List2 when they do not.
• Copying sx when the question wants σx (or the other way round).
• Running the regression on the wrong lists: SET still says List3 and List4 from an earlier Spearman question.
• Predicting with a and b rounded to 3 s.f., which can change the last figure of the estimate.
• Writing calculator words as working: write r = 0.998 and y = 3.83x + 43.8, not "LinReg".

1-minute quick check

Answer these without looking back. Most need no calculation: they check that the key presses have stuck.

1. Where do you set which lists 1-VAR uses?
2. Which one divides by n − 1: σx or sx?
3. Which keys give the linear regression line from the list editor?
4. How do you clear a whole list?
5. Is a prediction outside the range of the x data reliable?

Teaching this lesson (about 55 minutes)

Students need their own fx-CG50. With a projector, the calculator-skills guides below have a Show on the board view and an animated walkthrough of the key presses.

Matching calculator guides

• 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
• How to do linear, exponential, power, polynomial, sine and logistic regression on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
• How to find Pearson's r and Spearman's rank correlation on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II

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