Casio FX-7400G Plus Calculator
Contents
1. 2 General graph settings SET This section describes how to use the general graph settings screen to make the following settings for each graph GPH1 GPH2 GPH3 Graph Type The initial default graph type setting for all the graphs is scatter graph You can select one of a variety of other statistical graph types for each graph e List The initial default statistical data is List 1 for single variable data and List 1 and List 2 for paired variable data You can specify which statistical data list you want to use for x data and y data Frequency Normally each data item or data pair in the statistical data list is represented on a graph as a point When you are working with a large number of data items however this can cause problems because of the number of plot points on the graph When this happens you can specify a frequency list that contains values indicating the number of instances the frequency of the data items in the corresponding cells of the lists you are using for x data and y data Once you do this only one point is plotted for the multiple data items which makes the graph easier to read Mark Type This setting lets you specify the shape of the plot points on the graph 97 Statistical Graphs and Calculations Chapter 7 eTo display the general graph settings SET screen While the graph menu is on the display press SET to display the general graph settings screen F1 GRPH GF S2. 26275681 EAE The estimated value is displayed for yi 1000 116
3. Graphs and Calculations Chapter 7 P 99 G Type F3 Exp DRAW Med x2 The following are the meanings of the above parameters Bias Regression coefficient Dice Regression constant term gare Correlation coefficient E Power Regression Graph Exponential regression expresses y as a proportion of the power of x The standard power regression formula is y a x x so if we take the logarithms of both sides we get logy loga b x logx Next if we say X log x Y logy and a loga the formula corresponds to linear regression formula Y a bX E3 Pwr B 3313 1 17148 A 9655 y 3 x b COPY DRAW Fa DRAW Hed xA 108 Statistical Graphs and Calculations Chapter 7 P 102 G Type The following are the meanings of the above parameters Gh bse Regression coefficient Prsia Regression power Pass Correlation coefficient E Displaying Paired Variable Statistical Results Paired variable statistics can be expressed as both graphs and parameter values When these graphs are displayed the menu at the bottom of the screen appears as below Ce Lod Exp Fur evar F4 2VAR Paired variable calculation result menu Pressing 2VAR displays the following screen 2VAR Use to scroll the list so you can view the items that run off the bottom of the screen The following describes the meaning of each of the parameters E E AT Mean of xList data DN ATT
4. tus of two or all three of the graphs to draw On and then pressing DRAW After drawing the graphs you can select which graph formula to use when perform ing single variable statistic or regression calculations GRER z S Grehs On on ort DRAW 110 Statistical Graphs and Calculations Chapter 7 P 101 P 104 P 109 P 8 FA DRAW StatGrarhl Fi X i ee ee we dl FelectlTILe e The text at the top of the screen indicates the currently selected graph STAT Graph 1 Graph 1 STAT Graph 2 Graph 2 STAT Graph 3 Graph 3 1 Use and to change the currently selected graph The graph name at the top of the screen changes when you do StatGrarhs ee Felectl TILed 2 When graph you want to use is selected press 5 Linearkes a 4 66698 b 2 T3392 r 8 95611 Yoaxth COFT DRAW Now you can use the procedures under Displaying Single Variable Statistical Re sults and Displaying Paired Variable Statistical Results to perform statistical cal culations 5 Manual Graphing In all of the graphing examples up to this point values were calculated in accord ance with View Window settings and graphing was performed automatically This automatic graphing is performed when the S Wind item of the View Window is set to Auto auto graphing You can also produce graphs manually when the automatic graphing capabilities of this calculator cannot produce the re
5. Ascending sort P 84 SRT D Descending sort oEL MATN Mq 0 E P 81 Fi DEL Single data item delete P 82 F2 DEL A Delete all data P 82 F3 INS Insert data item Press to return to the previous menu P 78 The procedures you should use for data editing are identical to those you use with the list function For details see Chapter 6 List Function 2 Statistical Calculation Examples Once you input data you can use it to produce a graph and check for tendencies You can also use a variety of different regression calculations to analyze the data Example To input the following two data groups and perform statistical calculations 0 5 1 2 2 4 4 0 5 2 2 1 0 3 1 5 2 0 2 4 94 Statistical Graphs and Calculations Chapter 7 P 97 E inputting Data into Lists Input the two groups of data into List 1 and List 2 OUNHWWOB bs List I List E B2 0 0 e 0 e OO e OWOW amp OO SF by DOOBOBAOws GRP Hg CALC EETA ERTE Once data is input you can use it for graphing and statistical calculations Input values can be up to 10 digits long 9 digit mantissa and 2 digit exponent when using exponential format Values in statistical data table cells are shown only up to six digits You can use the and keys to move the highlighting to any cell in the lists for data input E Plotting Data Example To specify Graph 1 as non draw OFF and Graph 3 as draw
6. Chapter Statistical Graphs and Calculations This chapter describes how to input statistical data into lists and how to calculate the mean maximum and other statistical values It also tells you how to perform regression calculations Before Performing Statistical Calculations Statistical Calculation Examples Calculating and Graphing Single Variable Statistical Data Calculating and Graphing Paired Variable Statistical Data Manual Graphing Performing Statistical Calculations oa Pens Important This chapter contains a number of graph screen shots In each case new data values were input in order to highlight the particular characteristics of the graph being drawn Note that when you try to draw a similar graph the unit uses data values that you have input using the List function Because of this the graphs that appears on the screen when you perform a graphing operation will prob ably differ somewhat from those shown in this manual Statistical Graphs and Calculations Chapter 7 1 Before Performing Statistical Calculations In the Main Menu select the STAT icon to enter the STAT Mode and display the statistical data lists Use the statistical data lists to input data and to perform statistical calculations List WLizte Use and to move the highlighting around the lists P 95 Fi GRPH Graph menu P 113 F2 CALC Statistical calculation menu P 83 F3 SRT A
7. E Paired Variable Statistical Calculations In the previous examples from Linear Regression Graph to Power Regression Graph statistical calculation results were displayed after the scatter diagram was drawn These were numeric expressions of the characteristics of variables used in the graphic display The following operation produces the same values directly from the statistical data list F2 CALC F3 2VAR 7 Uariable 2I 126 J T Fi 1 z705 uar enar Aa E xch Now you can press and to view variable characteristics For details on the meanings of these statistical values see Displaying Paired Vari able Statistical Results E Regression Calculation In the explanations from Linear Regression Graph to Power Regression Graph regression calculation results were displayed after the graph was drawn Here the regression line and regression curve is represented by mathematical expressions You can directly determine the same expression from the data input screen Perform the following key operation E23 CALC F3 REG Linea kez E X 8 355555 4 275 r B 297Ts yoaxeth ETRE GSE T Single variable regression parameters are displayed Next you can use the following Fi X oo Linear regression F2 Med Med Med regression F3 X 2 Quadratic regression Fi Log Logarithmic regression F2 Exp Exponential regression F3 P
8. ET I aList YList Frea GFHL GFHE GF The settings shown here are examples only The settings on your general graph settings screen may differ eTo select the StatGraph area 1 While the general graph settings screen is on the display use and to move the highlighting to the StatGraph item GFHd GFHe GFHa A Bf A 2 Use the function key menu to select the StatGraph area you want to select Fi GPH1 Graph 1 F2 GPH2 Graph 2 F3 GPHS3 Graph 3 eTo select the graph type G Type 1 While the general graph settings screen is on the display use and to move the highlighting to the G Type item Scat xe E F3 2 Use the function key menu to select the graph type you want to select Fi Scat Scatter diagram EZ xy eee xy line graph Ce Hist Eos H Dis FE E F3 98 Statistical Graphs and Calculations Chapter 7 Fi Hist Histogram bar graph F2 Box Med box graph F3 NeDis Normal distribution curve Ce x Hea era FE E F3 Ce Fi X eee Linear regression graph F2 Med Med Med graph F3 X42 Quadratic regression graph Lea EzF Fur A A F3 Fi Log Logarithmic regression graph F2 Exp Exponential regression graph F3 Pwr Power regression graph Press to return to the previous menu eTo select the x axis data list XList 1 While the gra
9. F2 Exp Exponential regression graph F3 Pwr Power regression graph 2VAR Paired variable statistical results Press to return to the previous menu E Displaying Statistical Calculation Results Whenever you perform a regression calculation the regression formula parameter such as a and b in the linear regression y ax b calculation results appear on the display You can use these to obtain statistical calculation results Regression parameters are calculated as soon as you press a function key to select a regression type while a graph is on the display Example To display logarithmic regression parameter calculation results while a scatter diagram is on the display Fi Log E Graphing statistical calculation results You can use the parameter calculation result menu to graph the displayed regres sion formula COPY DRA E3 F3 COPY Stores the displayed regression formula as a graph function DRAW Graphs the displayed regression formula 102 Statistical Graphs and Calculations Chapter 7 P 101 P 99 G Type Hist P 95 P 99 G Type Box Example To graph a logarithmic regression While logarithmic regression parameter calculation results are on the display press DRAW Fa DRAW Mea fee For details on the meanings of function menu items at the bottom of the display see Selecting the Regression Type 3 Calculating
10. ON and use Graph 3 to plot the data you input into statistical data List 1 and List 2 above While the statistical data list is on the display press GRPH to display the graph menu Fi GRPH A 6 E3 Fi GPH1 Graph 1 draw F2 GPH2 Graph 2 draw F3 GPH3 Graph 3 draw Ce SEL SET EJ Fi SEL Graph GPH1 GPH2 GPHS3 selection F4 SET Graph settings graph type list assignments Press to return to the previous menu e You can specify the graph draw non draw status the graph type and other gen eral settings for each of the graphs in the graph menu GPH1 GPH2 GPH3 e You can press any function key F1 F2 F3 to draw a graph regardless of the current location of the highlighting in the statistical data list The initial default graph type setting for all the graphs Graph 1 through Graph 3 is scatter diagram but you can change to one of a number of other graph types 95 Statistical Graphs and Calculations Chapter 7 E Plotting a Scatter Diagram It is often difficult to spot the relationship between two sets of data such as height and shoe size by simply looking at the numbers Such relationships often become clear however when we plot the data on a graph using one set as x values and the other set as y values eTo plot a scatter diagram Example To plot the data we input in statistical data List 1 and List 2 Fi GPH1 x Thea ee The de
11. Sum of xList data Sum of squares of xList data Population standard deviation of xList data Sample standard deviation of xList data Number of xList data items Mean of yList data Sum of yList data Sum of squares of yList data Population standard deviation of yList data Sample standard deviation of yList data Sum of xList and yList data Minimum of xList data Maximum of xList data Minimum of yList data Maximum of yList data 109 Statistical Graphs and Calculations Chapter 7 P 96 E Copying a Regression Graph Formula to the Graph Mode After you perform a regression calculation you can copy its formula to the GRAPH Mode The following are the functions that are available in the function menu at the bottom of the display while regression calculation results are on the screen F3 COPY Stores the displayed regression formula to the GRAPH Mode DRAW Graphs the displayed regression formula 1 Press F3 COPY to copy the regression formula that produced the displayed data to the GRAPH Mode F3 COPY 4 StLorelCExEI Note that you cannot edit regression formulas for graph formulas in the GRAPH Mode 2 Press to save the copied graph formula and return to the previous regression calculation result display E Multiple Graphs You can draw more than one graph on the same display by using the procedure under Changing Graph Parameters to set the graph draw On non draw Off sta
12. and Graphing Single Variable Statistical Data Single variable data is data with only a single variable If you are calculating the average height of the members of a class for example there is only one variable height Single variable statistics include distribution and sum The following three types of graphs are available for single variable statistics E Drawing a Histogram Bar Graph From the statistical data list press Fi GRPH to display the graph menu press SET and then change the graph type of the graph you want to use GPH1 GPH2 GPH3 to histogram bar graph Data should already be input in the statistical data list see Inputting Data into Lists Draw the graph using the procedure described under Plotting Data E Box Graph This type of graph lets you see how a large number of data items are grouped within specific ranges A box encloses all the data in an area from the 25th percentile to the 75th percentile with a line drawn at the 50th percentile Lines called whiskers ex tend from either end of the box up to the minimum and maximum of the data From the statistical data list press Fi GRPH to display the graph menu press SET and then change the graph type of the graph you want to use GPH1 GPH2 GPH3 to box graph 103 Statistical Graphs and Calculations Chapter 7 P 99 G Type NeDis tT 4 LAK E Normal Distribution Curve The normal distribution cur
13. ed graph intercept E Quadratic Regression Graph A quadratic regression graph represents connection of the data points of a scatter diagram It actually is a scattering of so many points that are close enough together to be connected The formula that represents this is quadratic regression E3 X 2 Yoaxet bhoateo COFY DRAW 106 Statistical Graphs and Calculations Chapter 7 P 99 G Type P 99 G Type Fa DRAW xO Hed x2 The following are the meanings of the above parameters leer Regression second coefficient Dis oes Regression first coefficient Cras Regression constant term intercept E Logarithmic Regression Graph Logarithmic regression expresses y as a logarithmic function of x The standard logarithmic regression formula is y a b x logx so if we say that X logx the formula corresponds to linear regression formula y a bX E Log DRAW x Hed x2 The following are the meanings of the above parameters Avie Regression constant term intercept Daras Regression coefficient slope E Correlation coefficient E Exponential Regression Graph Exponential regression expresses y as a proportion of the exponential function of x The standard exponential regression formula is y a X e so if we take the loga rithms of both sides we get logy loga bx Next if we say Y logy and a loga the formula corresponds to linear regression formula Y a bx 107 Statistical
14. fault setting automatically uses List 1 data as x axis values and List 2 data as y axis values Each set of x y data is a point on the scatter diagram e To return to the statistical data list press un E Changing Graph Parameters Use the following procedures to specify the graph draw non draw status the graph type and other general settings for each of the graphs in the graph menu GPH1 GPH2 GPH3 1 Graph draw non draw status SELECT The following procedure can be used to specify the draw On non draw Off status of each of the graphs in the graph menu eTo specify the draw non draw status of a graph 1 While the graph menu is on the display press F1 SEL to display the graph On Off screen F1 GRPH FI SEL brehe on ore DRAW E E3 Fi On Graph On graph draw ED Off Graph Off graph non draw DRAW Draw all On graphs e Note that the S Grph1 setting is for Graph 1 GPH1 of the graph menu S Grph2 is for Graph 2 and S Grph3 is for Graph 3 96 Statistical Graphs and Calculations Chapter 7 2 Use and to move the highlighting to the graph whose draw On non draw Off status you want to change and press F1 On or F3 Off 3 To return to the graph menu press gum eTo draw a graph Example To draw a scatter diagram of Graph 3 only Fi GRPH B Fi SEL an Sireh S Dr EF On on ort DRA A F3 FI DRAW Mea fee
15. ist2 List 2 data is frequency data List List 3 data is frequency data EJ F3 E3 Listy ListS Liste 0 aA A 100 Statistical Graphs and Calculations Chapter 7 P 98 G Type xy Fi List4 List 4 data is frequency data FQ List5 List 5 data is frequency data F3 List6 List 6 data is frequency data Press to return to the previous menu eTo select the plot mark type M Type 1 While the general graph settings screen is on the display use and to move the highlighting to the M Type item REALE AA B f 2 Use the function key menu to select the plot mark you want to select Plot using Plot using X Plot using E Drawing an xy Line Graph Paired data items can be used to plot a scatter diagram A scatter diagram where the points are linked is an xy line graph Mea fee Press to return to the statistical data list E Selecting the Regression Type After you graph statistical data you can use the function menu at the bottom of the display to select from a variety of different types of regression x Hea era 0 a F ED X oe Linear regression graph F2 Med Med Med graph F3 X 2 Quadratic regression graph 101 Statistical Graphs and Calculations Chapter 7 P 110 Ce oes Exp Fur evar a a F3 Fi Log Logarithmic regression graph
16. nder Plotting a Scatter Diagram we displayed a scatter diagram and then per formed a logarithmic regression calculation Lets use the same procedure to look at the six regression functions M E Linear Regression Graph P 98 Linear regression plots a straight line that passes close to as many data points as possible and returns values for the slope and y intercept y coordinate when x 0 of the line The graphic representation of this relationship is a linear regression graph G Type un F GRPH B F4 SET Linearkea Scat Fi Scat a 8 62748 GPH1 aut F1 GRPH Fi GPH1 a Soe x B yoarth COFT DIRAL DRAW Hed x2 105 Statistical Graphs and Calculations Chapter 7 P 99 G Type P 99 G Type The following are the meanings of the above parameters eee Regression coefficient slope Boeie Regression constant term intercept Psie Correlation coefficient E Med Med Graph When it is suspected that there are a number of extreme values a Med Med graph can be used in place of the least squares method This is also a type of linear regres sion but it minimizes the effects of extreme values It is especially useful in produc ing highly reliable linear regression from data that includes irregular fluctuations such as seasonal surveys E3 Meo F4 DRAW O Hed xA The following are the meanings of the above parameters e Med Med graph slope Bice Med M
17. ocated before you start a calculation While the statistical data is on the display perform the following procedure F2 CALC F4 SET The following is the meaning for each item NNa X irena Specifies list where single variable statistic x values XList are located IVar E erissa Specifies list where single variable frequency values Fre quency are located ONAIX cisini Specifies list where paired variable statistic x values XList are located ONAIN A E Specifies list where paired variable statistic y values YList are located 2At F assises Specifies list where paired variable frequency values Fre quency are located e Calculations in this section are performed based on the above specifications E Single Variable Statistical Calculations In the previous examples from Histogram Bar Graph to Normal Distribution Curve statistical calculation results were displayed after the graph was drawn These were numeric expressions of the characteristics of variables used in the graphic display The following operation produces the same values directly from the statistical data list F2 CALC E1 1VAR i Variable 2a 1 Ba Sa 4 1 738 MAARE GSE Ty Now you can press and to view variable characteristics For details on the meanings of these statistical values see Displaying Single Vari able Statistical Results 113 Statistical Graphs and Calculations Chapter 7 P 109
18. ph settings screen is on the display use and to move the highlighting to the XList item ListalListalListalList4 AB A 2 Use the function key menu to select the name of the statistical data list whose values you want on the x axis of the graph Fi List1 List 1 FQ List2 List 2 F3 List List 3 List4 List 4 List5 List FA List5 List 5 A A FQ List6 List 6 Press to return to the previous menu 99 Statistical Graphs and Calculations Chapter 7 eTo select the y axis data list YList 1 While the graph settings screen is on the display use and to move the highlighting to the YList item Lis talListelcistallist4 A a 2 Use the function key menu to select the name of the statistical data list whose values you want on the y axis of the graph FA List1 List 1 FQ List2 List 2 F3 List3 List 3 List4 List 4 List5 Liste F F FA List5 List 5 FQ List6 List 6 Press to return to the previous menu eTo select the frequency data list Frequency 1 While the general graph settings screen is on the display use and to move the highlighting to the Frequency item Frea ti a listillistaliists A a F3 2 Use the function key menu to select the frequency setting you want ETTET Plot all data 1 to 1 List1 List 1 data is frequency data L
19. sults you want E Setting the Width of a Histogram When the S Wind item of the View Window is set to Man manual graphing a screen appears so you can specify the starting point and spacing of histogram bars 111 Statistical Graphs and Calculations Chapter 7 While the statistical data list is on the display perform the following procedure EE Furn e r Anale iRad Disrlar Hrmi Auty Harn E2 Man n Returns to previous menu E1 GRPH F1 GPH1 Here we will illustrate this operation by making histogram settings for Graph 1 Set Interval Strt 1 86836 eel a The following are the meanings of the items that appear in this screen SOUS einat Histogram start point x coordinate olie erent error Bar spacing specify as scale unit Example Strt 0 ptch 10 While the statistical data list is on the display perform the following procedure Fa Man un Returns to previous menu F GRPH F1 GPH1 0 E9 Start value is x 0 E pitch 10 112 Statistical Graphs and Calculations Chapter 7 P 104 6 Performing Statistical Calculations All of the statistical calculations up to this point were performed after displaying a graph The following procedures can be used to perform statistical calculations alone eTo specify statistical calculation data lists You have to input the statistical data for the calculation you want to perform and specify where it is l
20. ve is graphed using the following normal distribution func tion x x y it e 2x0 2 T xOn The distribution of characteristics of items manufactured according to some fixed standard such as component length fall within normal distribution The more data items there are the closer the distribution is to normal distribution From the statistical data list press Fi GRPH to display the graph menu press SET and then change the graph type of the graph you want to use GPH1 GPH2 GPH3 to normal distribution LURK E Displaying Single Variable Statistical Results Single variable statistics can be expressed as both graphs and parameter values When these graphs are displayed the menu at the bottom of the screen appears as below LUAR EJ Fi 1VAR Single variable calculation result menu Pressing Fi 1VAR displays the following screen F 1 VAR Statistical Graphs and Calculations Chapter 7 The following describes the meaning of each of the parameters E E EE Mean of data ATT Sum of data REE T Sum of squares Population standard deviation AEE Sample standard deviation E E E Number of data items MINA eias Minimum OT seein First quartile Medi sient Median QJ nisin Third quartile MAXX ersan Maximum MOG wieeen enced Mode e Press DRAW to return to the original single variable statistical graph 4 Calculating and Graphing Paired Variable Statistical Data U
21. wr Power regression The meanings of the parameters that appear on this screen are the same as those for Linear Regression Graph to Power Regression Graph 114 Statistical Graphs and Calculations Chapter 7 E Estimated Value Calculation x 5 After drawing a regression graph with the STAT Mode you can use the RUN Mode to calculate estimated values for the regression graph s x and y parameters e Note that you cannot obtain estimated values for Med Med graph and quad ratic regression graph Example To perform power regression using the following data and estimate the values of and when xi 40 and yi 1000 xi List 1 yi List 2 28 2410 30 3033 33 3895 35 4491 38 5717 1 In the Main Menu select the STAT icon and enter the STAT Mode 2 Input data into the list and draw the power regression graph G Type F GRPH FA SET Scat Scat XList List1 YList F2 List2 Freq FI 1 x Hed Kez M Type o qui Auto Cry Eu F4 Auto aur F1 GRPH Fd GPH1 Pwr F3 Pwr Fa DRAW 3 In the Main Menu select the RUN icon and enter the RUN Mode 4 Press the keys as follows 4 0 value of xi 403 en F3 STAT F3 E9 6387 674599 115 Statistical Graphs and Calculations Chapter 7 The estimated value is displayed for xi 40 0 0 value of yi Fi x amp qg BsS7 674559 20
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