Chapter 6 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.
6-1-1 Before Performing Statistical Calculations 6-1 Before Performing Statistical Calculations From the Main Menu, enter the STAT Mode and display the statistical data lists. Use the statistical data lists to input data and to perform statistical calculations. Use f, c, d and e to move the highlighting around the lists. 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.
6-1-2 Before Performing Statistical Calculations k 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). While the statistical data list is on the display, press 1(GRPH) to display the graph menu, which contains the following items. • {S-Gph1}/{S-Gph2}/{S-Gph3} ... graph {1}/{2}/{3} drawing*1 • {Select} ...
6-1-3 Before Performing Statistical Calculations • Mark Type This setting lets you specify the shape of the plot points on the graph. u To display the general graph settings screen [GRPH]-[Set] Pressing 1(GRPH)f(Set) displays the general graph settings screen. • The settings shown here are examples only. The settings on your general graph settings screen may differ. • StatGraph (statistical graph specification) • {GPH1}/{GPH2}/{GPH3} ...
6-1-4 Before Performing Statistical Calculations 2. Graph draw/non-draw status [GRPH]-[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. u To specify the draw/non-draw status of a graph 1. Pressing 1(GRPH) e(Select) displays the graph On/Off screen. • Note that the StatGraph1 setting is for Graph 1 (GPH1 of the graph menu), StatGraph2 is for Graph 2, and StatGraph3 is for Graph 3. 2.
-2-1 Calculating and Graphing Single-Variable Statistical Data 6-2 Calculating 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 types of graphs are available for single-variable statistics.
6-2-2 Calculating and Graphing Single-Variable Statistical Data k Med-box or Box and Whisker Graph (Box) 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 first quartile (Q1) to the third quartile (Q3), with a line drawn at the median (Med). Lines (called whiskers) extend from either end of the box up to the minimum (minX) and maximum (maxX) of the data.
6-2-3 Calculating and Graphing Single-Variable Statistical Data k Normal Distribution Curve (N • Dis) The normal distribution curve is graphed using the following normal distribution function. y= 1 (2 π) xσn e – (x–x) 2 2xσn 2 XList specifies the list where the data is input, while Freq specifies the list where the data frequency is input. 1 is specified for Freq when frequency is not specified. k Broken Line Graph (Brkn) Lines connect center points of a histogram bar.
6-2-4 Calculating and Graphing Single-Variable Statistical Data k Displaying the Calculation Results of a Drawn Single-Variable Graph Single-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the single-variable calculation results appear as shown below when you press 4(CALC)b(1VAR). • Use c 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. o ...........
6-3-1 Calculating and Graphing Paired-Variable Statistical Data 6-3 Calculating and Graphing Paired-Variable Statistical Data k Drawing a Scatter Diagram and xy Line Graph Description The following procedure plots a scatter diagram and connects the dots to produce an xy line graph. Set Up 1. From the Main Menu, enter the STAT Mode. Execution 2. Input the data into a list. 3. Specify Scat (scatter diagram) or xy (xy line graph) as the graph type, and then execute the graph operation.
6-3-2 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and connect the dots to produce an xy line graph. 0.5, 1.2, 2.4, 4.0, 5.2, (xList) –2.1, 0.3, 1.5, 2.0, 2.4 (yList) Procedure 1 m STAT 2 a.fwb.cw c.ewewf.cw e -c.bwa.dw b.fwcwc.
6-3-3 Calculating and Graphing Paired-Variable Statistical Data k Drawing a Regression Graph Description Use the following procedure to input paired-variable statistical data, perform a regression calculation using the data, and then graph the results. Set Up 1. From the Main Menu, enter the STAT Mode. Execution 2. Input the data into a list, and plot the scatter diagram. 3. Select the regression type, execute the calculation, and display the regression parameters. 4. Draw the regression graph.
6-3-4 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below and plot the data on a scatter diagram. Next, perform logarithmic regression on the data to display the regression parameters, and then draw the corresponding regression graph. 0.5, 1.2, 2.4, 4.0, 5.2, (xList) –2.1, 0.3, 1.5, 2.0, 2.4 (yList) Procedure 1 m STAT 2 a.fwb.cw c.ewewf.cw e -c.bwa.dw b.fwcwc.
6-3-5 Calculating and Graphing Paired-Variable Statistical Data k Selecting the Regression Type After you graph paired-variable statistical data, press 4(CALC). Then you can use the function menu at the bottom of the display to select from a variety of different types of regression. • {2VAR} ... {paired-variable statistical results} • {Linear}/{MedMed}/{Quad}/{Cubic}/{Quart}/{Log}/{Exp}/{Power}/{Sin}/{Lgstic} ...
6-3-6 Calculating and Graphing Paired-Variable Statistical Data k Linear Regression Graph Linear regression uses the method of least squares to plot 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. 4(CALC)c(Linear) 6(DRAW) The following is the linear regression model formula. y = ax + b a .............
6-3-7 Calculating and Graphing Paired-Variable Statistical Data k Quadratic/Cubic/Quartic Regression Graph A quadratic/cubic/quartic regression graph represents connection of the data points of a scatter diagram. It uses the method of least squares to draw a curve that passes close to as many data points as possible. The formula that represents this is quadratic/cubic/quartic regression. Ex. Quadratic regression 4(CALC)e(Quad) 6(DRAW) Quadratic regression Model formula ..... y = ax2 + bx + c a ..........
6-3-8 Calculating and Graphing Paired-Variable Statistical Data k Logarithmic Regression Graph Logarithmic regression expresses y as a logarithmic function of x. The standard logarithmic regression formula is y = a + b × In x, so if we say that X = In x, the formula corresponds to linear regression formula y = a + bX. 4(CALC)h(Log) 6(DRAW) The following is the logarithmic regression model formula. y = a + b • ln x a ............. regression constant term b ............. regression coefficient r ..........
6-3-9 Calculating and Graphing Paired-Variable Statistical Data k Power Regression Graph Power regression expresses y as a proportion of the power of x. The standard power regression formula is y = a × xb, so if we take the logarithm of both sides we get In y = In a + b × In x. Next, if we say X = In x, Y = In y, and A = In a, the formula corresponds to linear regression formula Y = A + bX. 4(CALC)j(Power) 6(DRAW) The following is the power regression model formula. y = a • xb a .............
6-3-10 Calculating and Graphing Paired-Variable Statistical Data k Logistic Regression Graph Logistic regression is best applied for time-based phenomena in which there is a continual increase until a saturation point is reached. The following is the logistic regression model formula. y= c 1 + ae–bx 4(CALC)l(Lgstic) 6(DRAW) • Certain types of data may take a long time to calculate. This does not indicate malfunction.
6-3-11 Calculating and Graphing Paired-Variable Statistical Data k Displaying the Calculation Results of a Drawn Paired-Variable Graph Paired-variable statistics can be expressed as both graphs and parameter values. When these graphs are displayed, the paired-variable calculation results appear as shown below when you press 4(CALC)b(2VAR). • Use c to scroll the list so you can view the items that run off the bottom of the screen. o ............... mean of data stored in xList Σ x .............
6-3-12 Calculating and Graphing Paired-Variable Statistical Data k 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) status of two or all three of the graphs to draw On, and then pressing 6(DRAW)(see page 6-1-4). After drawing the graphs, you can select which graph formula to use when performing singlevariable statistic or regression calculations.
6-3-13 Calculating and Graphing Paired-Variable Statistical Data k Overlaying a Function Graph on a Statistical Graph Description You can overlay a paired-variable statistical graph with any type of function graph you want. Set Up 1. From the Main Menu, enter the STAT Mode. Execution 2. Input the data into a list, and draw the statistical graph. 3. Display the Graph Function menu, and input the function you want to overlay on the statistical graph. 4. Graph the function.
6-3-14 Calculating and Graphing Paired-Variable Statistical Data ○ ○ ○ ○ ○ Example Input the two sets of data shown below. Next, plot the data on a scatter diagram and overlay a function graph y = 2ln x. 0.5, 1.2, 2.4, 4.0, 5.2, –2.1, 0.3, 1.5, 2.0, 2.4 Procedure 1 m STAT 2 a.fwb.cw c.ewewf.cw e -c.bwa.dw b.fwcwc.ew 1(GRPH)b(S-Gph1) 3 5(DefG) cIvw(Register Y1 = 2In x) 4 6(DRAW) Result Screen # You can also perform trace, etc. for drawn function graphs.
6-4-1 Performing Statistical Calculations 6-4 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. u To specify statistical calculation data lists You have to input the statistical data for the calculation you want to perform and specify where it is located before you start a calculation. Display the statistical data and then press 2(CALC)e(Set).
6-4-2 Performing Statistical Calculations k Single-Variable Statistical Calculations In the previous examples from “Normal Probability Plot” and “Histogram (Bar Graph)” to “Line Graph,” statistical calculation results were displayed after the graph was drawn. These were numeric expressions of the characteristics of variables used in the graphic display. These values can also be directly obtained by displaying the statistical data list and pressing 2(CALC)b(1VAR).
6-4-3 Performing Statistical Calculations k Regression Calculation In the explanations from “Linear Regression Graph” to “Logistic Regression Graph,” regression calculation results were displayed after the graph was drawn. Here, each coefficient value of the regression line and regression curve is expressed as a number. You can directly determine the same expression from the data input screen. Pressing 2(CALC)d(REG) displays the pull-up menu, which contains the following items.
6-4-4 Performing Statistical Calculations k Estimated Value Calculation ( , ) After drawing a regression graph with the STAT Mode, you can use the RUN • MAT Mode to calculate estimated values for the regression graph's x and y parameters. ○ ○ ○ ○ ○ Example To perform a linear regression using the nearby data and estimate the values of and when xi = 20 and yi = 1000 xi yi 10 15 20 25 30 1003 1005 1010 1011 1014 1. From the Main Menu, enter the STAT Mode. 2.
6-4-5 Performing Statistical Calculations k Normal Probability Distribution Calculation You can calculate normal probability distributions for single-variable statistics with the RUN • MAT Mode. Press K6(g)1(PROB) to display a function menu, which contains the following items. • {P(}/{Q(}/{R(} ... obtains normal probability {P(t)}/{Q(t)}/{R(t)} value • {t(} ...
6-4-6 Performing Statistical Calculations 1. Input the height data into List 1 and the frequency data into List 2. 2. Perform the single-variable statistical calculations.*1 2(CALC)e(Set) 1(LIST)bw c2(LIST)cwi 2(CALC)b(1VAR) 3. Press m, select the RUN • MAT Mode, press K6(g)1(PROB) to recall the probability calculation (PROB) menu. 1(PROB)i( t() bga.f)w (Normalized variate t for 160.5cm) 1(PROB)i(t() bhf.f)w (Normalized variate t for 175.5cm) 1(PROB)f(P()a.ejg)1(PROB)f(P()-b.
6-4-7 Performing Statistical Calculations k Drawing a Normal Probability Distribution Graph Description You can draw a normal probability distribution graph using manual graphing with the RUN • MAT Mode. Set Up 1. From the Main Menu, enter the RUN • MAT Mode. Execution 2. Input the commands to draw a rectangular coordinate graph. 3. Input the probability value.
6-4-8 Performing Statistical Calculations ○ ○ ○ ○ ○ Example To draw a normal probability P (0.5) graph. Procedure 1 m RUN • MAT 2 K6(g)6(g)2(SKTCH)b(Cls)w 2(SKTCH)e(GRPH)b(Y=) 3 K6(g)1(PROB)f(P()a.
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