Casio ClassPad Core - haesemathematics.com

1 Casio ClasspadReplacement calculator screens for the Core material Chapter 1: Univariate data Page 30 Using the calculator to find the mean, median and modeUse the calculator to find the mean and median of the following data : 2, 3, 5, 4, 3, 6, 5, 7, 3, 8, 1, 7, 5, 5, 9 Tap on the Statistics icon I in the applications menu. Uselist 1; check that the cursor is in the first position of list into the first position; this value will appear at the bottom of the screen as [ 1] = 2. Key E to move to the next position in the list. Type the remaining data values into list 1 keying Eafter each entry. Note: There are 15 data values in the set so the screen shows all the data is entered in list 1. To find the descriptive statistics for the data Tap Calc in the menu bar to get you into the menus for finding descriptive statistics. We are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the list that contains the relevant data .

2 Tap OK All the available descriptive statistics for this variable appear on the screen :- On this screen the first statistic, , is the mean. The mean of the data is (to 3 decimal places) The second statistic: x = 73 means that the sum of the data v all k symbol meaning alues as 73; the Gree5 refers to the fact that there are ticsber summary hich is covered in section 1F sum of . The next three statistics we will consider in section 1E. n = 115 data values in the set. Scroll down to access other statisMed = 5 means the median is 5 Mode = 5 gives the mode for this data set The other statistics on this part of the screenare the statistics of the five-numw1 Page 34 Using the calculator to find the range and inter-quartile range: Key the data into a list. The data does not have to be ordered. Tap Calc in the menu bar to get you into the menus for finding descriptive statistics. We are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the list that contains the relevant data .

3 Tap OK The screens at right show all the statistics for the data . Scrolling down will reveal the lower part of the range is maxX minX = 14 3 = 11 The IQR = Q3 Q1 = 9 5 = 4 Page 38 Using the calculator to find the standard deviation Key the data into a list. Tap Calc in the menu bar to get you into the menus for finding descriptive are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the list that contains the relevant data . TapOK2 The sample standard deviation that we use is The sample standard deviation is Note: Thevariance is not given on the screen. The variance can be found by squaring the standard deviation. Page 38 Standard deviation for grouped data Key the data into the lists using list 1 for the data values and list 2 for the frequency. Tap Calc in the menu bar to get you into the menus for finding descriptive are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the lists that contains the data (list 1) and the frequency (list 2)TapOKThe sample standard deviation that we use is The sample mean is and the sample standarddeviation is 47 Using the graphing calculator to find descriptive statistics and construct a the data from the example above: 2, 3, 5, 4, 3, 6, 5, 7, 3, 8, 1, 7, 5, 5, 9 Key the data into a onTap on SetGraph in the menu bar and tap access the Set StatGraphs screen TurnDraw OnThe type of graph is a MedBoxThe data is in list 1 Tick the Show Outliers box.

4 TapSet to get back to the lists screen Tap the graph icon y to display the boxplot in the bottom half of the screen . TapAnalysis in the menu bar and select Tracethen use the cursor keys to see the values of the five number summary displayed on the graph. 4 Page 50 Example 20 Using the calculator: Page 51 Using the calculator to draw the boxplot in Example 20. Tap on SetGraph and tap access the Set StatGraphs screen TurnDraw onThe type of graph is a MedBoxThe data is in list 1 Tick the Show Outliers box. TapSet to get back to the lists screen Tap the graph icon y to display the boxplot in the bottom half of the screen . TapAnalysis in the menu bar and choose Tracethen the cursor keys to seethe values of the five number summary displayed on the graph. Page 55 Using the random number generator on the calculator: Go to the Main menu Jand press the Keyboardk .Access the catalogue by tapping on (Tap twice for rand( to appear on the in the range of integers that we are considering1,45) and then tap EXE Other random numbers in the same range can be obtained by tapping EXE repeatedly.)

5 5To obtain a list of six random numbers in the range 1 to 45 inclusive i. Locate randList in the catalogue. Tap twice to forrandList( to appear on the screen. ii. Type in 6,1,45) ; the number of random numbers required and the range of numbers, all separated by commas. Close the bracket and press EXEA list of six random numbers in the range 1 to 45 will be generated. Other sets of random numbers in the same range can be found by tapping repeatedly EXEPage 56 Example 21 Core Chapter 2 : Bivariate data Page 63 Using the calculator to graph parallel boxplots. Enter the data into the lists:Tap on SetGraph and tap access the Set StatGraphs screen Set-up the first boxplot: TurnDraw onThe type of graph is a MedBoxThe data is in list 1 Tick the Show Outliers box. Set-up the second boxplot: Tap on the 2 for the second graph The data for the second graph is in list set-up the third graph ; the data for the third graph is in list setting-up all three graphs tap on Set6 Tap on the graph icon y to produce the parallel boxplots.

6 Tap the Resize option at the bottom of the screen to get a full screen graph. Page 69 Using the calculator to construct a scatterplot Enter the data into the lists; the independent variable (height) inlist 1and the dependent variable (weight) inlist 2 Tap on SetGraph and tap access the Set StatGraphs screen Set-up the graph as shown, tapping Set to get back to the lists screen. Tap on the graph icon to produce the graph. TappingAnalysis, then Trace and then using the cursor keys allows you to identify the points. Page 75 Using the calculator to find Pearson s correlation coefficient EnterEnter the data into the lists; the independent variable inlist 1and the dependent variable inlist 2 Produce a scatterplot for the data ; it will reveal any errors made in entering the data and any outliers. It will also indicate whether the data is linear. The scatterplot indicates strong, positive, linear correlation between the variables. 7 Tap on Calc and then on Linear Reg This means that we are fitting a linear model or linear regression of the form y = ax + b to the data .

7 Regression will be discussed in greater detail in Chapter 3 Complete the Set Calculation screen as shown, tapping OK when finished. The appropriateStat Calculation screen will appear. The linear regression screen for this data is shown at right. Pearson s correlation coefficient r is this example. Thisr value indicates a strong, positive correlationas indicated by the scatterplot. Page 78 Calculation of the coefficient of determination. r2is found on the linear regression screen of the calculator. r2 = Alternatively, if the value of r is known, then this can simply be squared. Core Chapter 3 : Linear regression Page 88 Using the calculator to find the three median regression line. Enter the data into the lists and draw a scatterplot to make sure the data is entered correctly. TapCalc from the menu bar and select MedMed the Set Calculationsscreen as shown at right: 8 Tap OK and the coefficients for the equation of the three- median regression line are shown.

8 The equation in this case is TapOK and the regression line appears on the 91 Using the calculator to find the least squares regression line. Enter the data into the lists and draw a scatterplot to make sure the data is entered correctly. TapCalc in the menu bar and select Linear Reg Complete the Set Calculationsscreen as shown at right: Tap OK The figures for Linear Regression appear on the screen. The values a and b are the coefficients for the equation of the least-squares regression is the slope of the line and b is the intercept. The equation is Note:Least squares regression lines are often written in the form which in this case would be The slope is always the number multiplying the independent variable and the least squares regression line appears on the scatterplot. 9 Page 98 Using the calculator to find and plot the residuals. Using the data from Page 91:TapCalc to access the Set Calculations screen. Choose LinearRegression. ChangeCopy Residual from Off to list 3.

9 This will paste the residual values into list 3. Tap OKTapSetGraph and go into graph 1 Tap on graph 2 and complete the settings as on Set and then the graph icon residual plot is shown on the lower half of the screen. 10 Page 104 Example 4 a. Enter the data into the lists and construct a scatterplot . The data does not appear to be linear. Fit a least-squares regression line to the data and construct a residual plot: From the menu bar tap Calc and the Complete the Set Calculations screen as shown. Tap Linear regression screen appears. Tap least squares regression line appears on the scatterplot. Tap the label of list 3 to fill the column with the residual values. Set-up graph 2 for the residual plot (turn graph 1 Off). Tap residual plot shows a pattern suggesting that the linear model is not the best fit. 11b. We can apply the x2transformation by adding an extra row containingx2 values in the table. To do this on the table go to the Callocation for list 4 and, using the keyboard, type in list1^ on the label of list 4 and the column will fill with the values from list 1, squared.

10 Go to SetGraph in the menu bar and choose to construct a scatterplot ofy(list 2) versus x2(list 4). TapSet and then the graph icon scatterplot of y versus x2 appears to be linear. Go to SetGraph and complete the Set Calculation screen so that the residuals for this transformed graph are in list 5. TapOK to see the Linear Regression screen and(TapOK) to fill list 5 with the and and complete the screen for graph 3 as shown (make sure the other graphs are turned Off)TapSet and the graph icon y to construct the residuals plot for the transformation. The residuals plot confirms that the relationship between y and x2 is linear. c. From the linear regression screen above we can write the equation. The slope, a, is and the intercept, b, is so the equation connecting yandx2 is Page 109 Example 5 a. Enter the data and construct a data is clearly not linear and has the general shape. We therefore consider the four transformations where x represents the day and y represents the audience size.