Casio FX-9750G User manual

Chapter
18
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.
18-1 Before Performing Statistical Calculations
18-2 Paired-Variable Statistical Calculation Examples
18-3 Calculating and Graphing Single-Variable Statistical
Data
18-4 Calculating and Graphing Paired-Variable Statistical
Data
18-5 Other Graphing Functions
18-6 Performing Statistical Calculations
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.

284
18-1 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.
1(GRPH) .... Graph menu
2(CALC)..... Statistical calculation menu
6(g) ........... Next menu
6(g)
1(SRT•A).... Ascending sort
2(SRT•D) ... Descending sort
3(DEL) ....... Single data item delete
4(DEL•A).... Delete all data
5(INS) ........ Insert data item
6(g) ........... Previous menu
• The procedures you should use for data editing are identical to those you use
with the list function. For details, see “17. List Function”.
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Use f, c, d and e to move
the highlighting around the lists.

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18-2 Paired-Variable 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
kk
kk
kInputting Data into Lists
Input the two groups of data into List 1 and List 2.
a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
Once data is input, you can use it for graphing and statistical calculations.
• Input values can be up to 10 digits long.
• You can use the f, c, dand ekeys to move the highlighting to any cell in
the lists for data input.
kk
kk
kPlotting Data
Example To specify Graph 1 as non-draw (Off) and Graph 3 as draw (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 1(GRPH) to display the graph
menu.
1(GRPH)
1(GPH1)..... Graph 1 draw
2(GPH2)..... Graph 2 draw
3(GPH3)..... Graph 3 draw
4(SEL)........ Graph (GPH1, GPH2, GPH3) selection
6(SET) ....... Graph settings (graph type, list assignments)
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• 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).
• You can press any function key (1,2,3) 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.
kk
kk
kPlotting 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.
uu
uu
uTo plot a scatter diagram
Example To plot the data we input in statistical data List 1 and List 2
1(GPH1)
• The default setting automatically uses List 1 data asx-axis values and List 2 data
as y-axis values. Each set of x/ydata is a point on the scatter diagram.
• To return to the statistical data list, press Jor !Q.
kk
kk
kChanging 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).
18 - 2 Paired-Variable Statistical Calculation Examples
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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.
uu
uu
uTo specify the draw/non-draw status of a graph
1. While the graph menu is on the display, press 4(SEL) to display the graph On/
Off screen.
1(GRPH)
4(SEL)
1(On).......... Graph On (graph draw)
2(Off).......... Graph Off (graph non-draw)
6(DRAW).... Draw all On graphs
• 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. Usefand cto move the highlighting to the graph whose draw (On)/non-draw
(Off) status you want to change and press 1(On) or 2(Off).
3. To return to the graph menu, press J.
uu
uu
uTo draw a graph
Example To draw a scatter diagram of Graph 3 only
1(GRPH)4(SEL)
2(Off)
cc1(On)
6(DRAW)
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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.
• List
The initial default is statistical data 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.
uu
uu
uTo display the general graph settings (SET) screen
While the graph menu is on the display, press 6(SET) to display the general graph
settings screen.
1(GRPH)
6(SET)
• The settings shown here are examples only. The settings on your general graph
settings screen may differ.
uu
uu
uTo select the StatGraph area
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the StatGraph item.
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2. Use the function key menu to select the StatGraph area you want to select.
1(GPH1)..... Graph 1
2(GPH2)..... Graph 2
3(GPH3)..... Graph 3
uu
uu
uTo select the graph type (Graph Type)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the Graph Type item.
2. Use the function key menu to select the graph type you want to select.
1(Scat) ....... Scatter diagram
2(xy)........... xy line graph
6(g) ........... Next menu
6(g)
1(Hist) ........ Histogram (bar graph)
2(Box) ........ Med-box graph
___
3(Box) ........ Mean-box graph
4(N•Dis) ..... Normal distribution curve
5(Brkn) ....... Line graph
6(g) ........... Next menu
6(g)
1(X) ............ Linear regression graph
2(Med) ....... Med-Med graph
3(X^2) ........ Quadratic regression graph
4(X^3) ........ Cubic regression graph
5(X^4) ........ Quartic regression graph
6(g) ........... Next menu
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6(g)
1(Log) ........ Logarithmic regression graph
2(Exp) ........ Exponential regression graph
3(Pwr) ........ Power regression graph
6(g) ........... Previous menu
uu
uu
uTo select the x-axis data list (XList)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the XList item.
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.
1(List1)....... List 1
2(List2)....... List 2
3(List3)....... List 3
4(List4)....... List 4
5(List5)....... List 5
6(List6)....... List 6
uu
uu
uTo select the y-axis data list (YList)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the YList item.
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.
1(List1)....... List 1
2(List2)....... List 2
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3(List3)....... List 3
4(List4)....... List 4
5(List5)....... List 5
6(List6)....... List 6
uu
uu
uTo select the frequency data list (Frequency)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the Frequency item.
2. Use the function key menu to select the frequency setting you want.
1(1) ............ Plot all data (1-to-1)
2(List1)....... List 1 data is frequency data.
3(List2)....... List 2 data is frequency data.
4(List3)....... List 3 data is frequency data.
5(List4)....... List 4 data is frequency data.
6(g) ........... Next menu
6(g)
1(List5)....... List 5 data is frequency data.
2(List6)....... List 6 data is frequency data.
6(g) ........... Previous menu
uu
uu
uTo select the plot mark type (Mark Type)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the Mark Type item.
2. Use the function key menu to select the plot mark you want to select.
1( ) ........... Plot using
2(X) ............ Plot using X
3(•) ............. Plot using •
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kk
kk
kDrawing 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.
Press Jor !Q to return to the statistical data list.
kk
kk
kSelecting 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.
1(X) ............ Linear regression graph
2(Med) ....... Med-Med graph
3(X^2) ........ Quadratic regression graph
4(X^3) ........ Cubic regression graph
5(X^4) ........ Quartic regression graph
6(g) ........... Next menu
6(g)
1(Log) ........ Logarithmic regression graph
2(Exp) ........ Exponential regression graph
3(Pwr) ........ Power regression graph
4(2VAR) ..... Paired-variable statistical results
6(g) ........... Previous menu
18 - 2 Paired-Variable Statistical Calculation Examples
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(GraphType)
(xy)
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kk
kk
kDisplaying Statistical Calculation Results
Whenever you perform a regression calculation, the regression formula parameter
(such as aand bin 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
6(g)1(Log)
kk
kk
kGraphing Statistical Calculation Results
You can use the parameter calculation result menu to graph the displayed regres-
sion formula.
5(COPY) .... Stores the displayed regression formula as a graph function
6(DRAW).... Graphs the displayed regression formula
Example To graph a logarithmic regression
While logarithmic regression parameter calculation results are on the display, press
6(DRAW).
6(DRAW)
For details on the meanings of function menu items at the bottom of the display, see
“Selecting the Regression Type”.
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18-3 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 five types of
graphs are available for single-variable statistics.
kk
kk
kDrawing a Histogram (Bar Graph)
From the statistical data list, press 1(GRPH) to display the graph menu, press 6
(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 List”).
Draw the graph using the procedure described under “Plotting Data”.
⇒
6(DRAW)
The display screen appears as shown above before the graph is drawn. At this
point, you can change the Start and pitch values.
kk
kk
kMed-box Graph (Med-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 25th percentile to the
75th percentile, with a line drawn at the 50th percentile. Lines (called whiskers)
extend from either end of the box up to the minimum and maximum of the data.
From the statistical data list, press 1(GRPH) to display the graph menu, press 6
(SET), and then change the graph type of the graph you want to use (GPH1, GPH2,
GPH3) to med-box graph.
kk
kk
kMean-box Graph
This type of graph shows the distribution around the mean when there is a large
number of data items.A line is drawn at the point where the mean is located, and
then a box is drawn so that it extends below the mean up to the standard deviation
and above the mean up to the standard deviation. Lines (called whiskers) extend
from either end of the box up to the minimum and maximum of the data.
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(Graph Type)
(Hist)
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(Graph Type)
(Box)
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(Box)

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From the statistical data list, press 1(GRPH) to display the graph menu, press 6
(SET), and then change the graph type of the graph you want to use (GPH1, GPH2,
GPH3) to mean-box graph.
kk
kk
kNormal Distribution Curve
The normal distribution curve is graphed using the following normal distribution func-
tion.
y= 1
(2π)xσ n
e
–2xσ
n
2
(x–x)
2
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 1(GRPH) to display the graph menu, press 6
(SET), and then change the graph type of the graph you want to use (GPH1, GPH2,
GPH3) to normal distribution.
kk
kk
kLine Graph
A line graph is formed by plotting the data in one list against the frequency of each
data item in another list and connecting the points with straight lines.
Calling up the graph menu from the statistical data list, pressing6(SET), changing
the settings to drawing of a line graph, and then drawing a graph creates a box
graph.
⇒
6(DRAW)
The display screen appears as shown above before the graph is drawn. At this
point, you can change the Start and pitch values.
Calculating and Graphing Single-Variable Statistical Data 18 - 3
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(Graph Type)
(N•Dis)
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(Graph Type)
(Brkn)
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Note :
This function is not usually used in
the classrooms in U.S. Please use
Med-box Graph, instead.

296
18 - 3 Calculating and Graphing Single-Variable Statistical Data
kk
kk
kDisplaying 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.
1(1VAR) ..... Single-variable calculation result menu
Pressing 1(1VAR) displays the following screen.
1(1VAR)
• Use cto 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.
_
x..................... Mean of data
Σx................... Sum of data
Σx2.................. Sum of squares
xσn.................. Population standard deviation
xσn-1 ................ Sample standard deviation
n..................... Number of data items
minX ............... Minimum
Q1 .................. First quartile
Med ................ Median
Q3 .................. Third quartile
_
x–xσn............ Data mean – Population standard deviation
_
x+xσn............ Data mean + Population standard deviation
maxX .............. Maximum
Mod ................ Mode
• Press 6(DRAW) to return to the original single-variable statistical graph.

297
18-4 Calculating and Graphing Paired-Variable
Statistical Data
Under “Plotting a Scatter Diagram,” we displayed a scatter diagram and then per-
formed a logarithmic regression calculation. Let’s use the same procedure to look at
the six regression functions.
kk
kk
kLinear Regression Graph
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.
!Q1(GRPH)6(SET)c
1(Scat)
!Q1(GRPH)1(GPH1)
1(X)
6(DRAW)
The following are the meanings of the above parameters.
a ...... Regression coefficient (slope)
b ...... Regression constant term (intercept)
r ...... Correlation coefficient
kk
kk
kMed-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.
2(Med)
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(Graph Type)
(Scatter)
(GPH1)
(X)
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6(DRAW)
The following are the meanings of the above parameters.
a ...... Med-Med graph slope
b ...... Med-Med graph intercept
kk
kk
kQuadratic/Cubic/Quartic Regression Graph
A quadratic/cubic/quartic 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/
cubic/quartic regression.
Ex. Quadratic regression
3(X^2)
6(DRAW)
The following are the meanings of the above parameters.
Quadratic regression
a ...... Quadratic regression coefficient
b ...... Linear regression coefficient
c ...... Regression constant term (intercept)
Cubic regression
a ...... Cubic regression coefficient
b ...... Quadratic regression coefficient
c ...... Linear regression coefficient
d ...... Regression constant term (intercept)
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Quartic regression
a ...... Quartic regression coefficient
b ...... Cubic regression coefficient
c ...... Quadratic regression coefficient
d ...... Linear regression coefficient
e ...... Regression constant term (intercept)
kk
kk
kLogarithmic Regression Graph
Logarithmic regression expresses yas a logarithmic function of x. The standard
logarithmic regression formula is y= a+ b×logx, so if we say that X = logx, the
formula corresponds to linear regression formula y= a+ bX.
6(g)1(Log)
6(DRAW)
The following are the meanings of the above parameters.
a ...... Regression constant term (intercept)
b ...... Regression coefficient (slope)
r ...... Correlation coefficient
kk
kk
kExponential Regression Graph
Exponential regression expresses yas a proportion of the exponential function of x.
The standard exponential regression formula is y= a×ebx, 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.
6(g)2(Exp)
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6(DRAW)
The following are the meanings of the above parameters.
a ...... Regression coefficient
b ...... Regression constant term
r ...... Correlation coefficient
kk
kk
kPower Regression Graph
Exponential regression expresses yas a proportion of the power of x. The standard
power regression formula is y= a×xb, so if we take the logarithms of both sides we
get logy= loga+ b×logx. Next, if we say X = log x, Y = logy, and a= loga, the
formula corresponds to linear regression formula Y = a+ bX.
6(g)3(Pwr)
6(DRAW)
The following are the meanings of the above parameters.
a ...... Regression coefficient
b ...... Regression power
r ...... Correlation coefficient
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kk
kk
kDisplaying 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.
4(2VAR) ...... Paired-variable calculation result menu
Pressing 4(2VAR) displays the following screen.
4(2VAR)
• Use cto 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.
_
x..................... Mean of xList data
Σx................... Sum of xList data
Σx2.................. Sum of squares of xList data
xσn.................. Population standard deviation of xList data
xσn-1 ................ Sample standard deviation of xList data
n..................... Number of xList data items
_
y..................... Mean of yList data
Σy................... Sum of yList data
Σy2.................. Sum of squares of yList data
yσn.................. Population standard deviation of yList data
yσn-1 ................ Sample standard deviation of yList data
Σxy ..................Sum of xList and yList data
minX ............... Minimum of xList data
maxX .............. Maximum of xList data
minY ............... Minimum of yList data
maxY .............. Maximum of yList data
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kk
kk
kCopying 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.
5(COPY) .... Stores the displayed regression formula to the GRAPH Mode
6(DRAW).... Graphs the displayed regression formula
1. Press 5(COPY) to copy the regression formula that produced the displayed
data to the GRAPH Mode.
5(COPY)
Note that you cannot edit regression formulas for graph formulas in the GRAPH
Mode.
2. Press wto save the copied graph formula and return to the previous regression
calculation result display.
kk
kk
kMultiple 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-
tus of two or all three of the graphs to draw (On), and then pressing 6(DRAW).
After drawing the graphs, you can select which graph formula to use when perform-
ing single-variable statistic or regression calculations.
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