Casio ALGEBRA FX 2.0 User manual

19990401
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.
6-1 Before Performing Statistical Calculations
6-2 Calculating and Graphing Single-Variable Statistical
Data
6-3 Calculating and Graphing Paired-Variable Statistical
Data
6-4 Performing Statistical Calculations
6-5 Distribution
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 appear on the screen when you perform a graphing
operation will probably differ somewhat from those shown in this manual.
6

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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.
kInputting Data into Lists
○○○○○
Example To input the following two data groups
0.5, 1.2, 2.4, 4.0, 5.2
–2.1, 0.3, 1.5, 2.0, 2.4
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.
6-1-1
Before Performing Statistical Calculations
# Except for complex numbers, calculation
results can be input as statistical data.
#You can use the f, c, dand ekeys
to move the highlighting to any cell in the lists
for data input.

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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).
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} ... {simultaneous graph (GPH1, GPH2, GPH3) selection} (You can specify the
multiple graphs.)
•{Set} ... {graph settings (graph type, list assignments)}
1. General graph settings [GRPH]-[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 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.
6-1-2
Before Performing Statistical Calculations
*1 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.
#You can 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).

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• Mark Type
This setting lets you specify the shape of the plot points on the graph.
uTo 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} ... graph {1}/{2}/{3}
• Graph Type (graph type specification)
•{Scat}/{xy}/{NPP} ... {scatter diagram}/{xy line graph}/{normal probability plot}
•{Hist}/{Box}/{ModB}/{N·Dis}/{Brkn} ... {histogram}/{med-box graph}/{modified-box
graph}/{normal distribution curve}/{line graph}
•{X}/{Med}/{X^2}/{X^3}/{X^4} ... {linear regression graph}/{Med-Med graph}/{quadratic
regression graph}/{cubic regression graph}/{quartic regression graph}
•{Log}/{Exp}/{Pwr}/{Sin}/{Lgst} ... {logarithmic regression graph}/{exponential regression
graph}/{power regression graph}/{sinusoidal regression graph}/{logistic regression graph}
• XList (x-axis data list)
•{LIST} ... {List 1 to 20}
• YList (y-axis data list)
•{LIST} ... {List 1 to 20}
• Frequency (number of times a value occurs)
•{1} ... {1-to-1 plot}
•{LIST} ... contents of these lists indicate the frequency of XList and YList data
• Mark Type (plot mark type)
•{ }/{×}/{•} ... scatter diagram plot points
6-1-3
Before Performing Statistical Calculations

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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.
uTo 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. Use the cursor keys to move the highlighting to the graph whose status you want to
change, and press the applicable function key to change the status.
•{On}/{Off} ... {On (draw)}/{Off (non-draw)}
•{DRAW} ... {draws all On graphs}
3. To return to the graph menu, press i.
6-1-4
Before Performing Statistical Calculations
#ViewWindow parameters are normally set
automatically for statistical graphing. If you
want to set View Window parameters
manually, you must change the Stat Wind item
to “Manual”.
While the statistical data list is on the display,
perform the following procedure.
u3(SET UP)2(Man)
i(Returns to previous menu.)
#The default setting automatically uses List 1
data as x-axis (horizontal) values and List 2
data as y-axis (vertical) values. Each set of x/y
data is a point on the scatter diagram.
# Pressinguadoes not hide the menu while a
statistical graph is on the display.

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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.
You can also use the procedures under “Changing Graph Parameters” on page 6-1-2 to make
the settings you want before drawing each graph.
kk
kk
kNormal Probability Plot (NPP)
This plot compares the data accumulated ratio with a normal distribution accumulated ratio.
XList specifies the list where data is input, and Mark Type is used to select from among the
marks { / ×/ •}you want to plot.
Press ior !i(QUIT) to return to the statistical data list.
kk
kk
kHistogram (Bar Graph) (Hist)
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.
6-2-1
Calculating and Graphing Single-Variable Statistical Data
⇒
w(Draw)
The display screen appears as shown above before the graph is drawn. At this point, you
can change the Start and pitch values.

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kMed-box 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 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.
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.
kModified Box Graph (ModB)
The modified box graph omits everything in the range past 1.5 ×IQR (IQR = Q3 – Q1,
Q3: 3rd quartile, Q1: 1st quartile) from the med-box 4th quartile and draws whiskers.
Outliers are displayed as plot points.
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.
6-2-2
Calculating and Graphing Single-Variable Statistical Data
#Input a positive integer for frequency data.
Other types of values (decimals, etc.) cause
an error.

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kNormal Distribution Curve (N •Dis)
The normal distribution curve is graphed using the following normal distribution function.
y
= 1
(2 π)xσ n
e
–2xσ
n
2
(x–x)
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.
kLine Graph (Brkn)
Lines connect center points of a histogram bar.
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.
6-2-3
Calculating and Graphing Single-Variable Statistical Data
⇒
w(Draw)
The display screen appears as shown above before the graph is drawn. At this point, you
can change the Start and pitch values.

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kDisplaying 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 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.
o............. mean
Σx........... sum
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
maxX ...... maximum
Mod ........ mode
Mod : n ... number of data mode items
Mod : F ... data mode frequency
•Press 6(DRAW) to return to the original single-variable statistical graph.
6-2-4
Calculating and Graphing Single-Variable Statistical Data
#When Mod has multiple solutions, they are all
displayed.

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6-3-1
Calculating and Graphing Paired-Variable Statistical Data
6-3 Calculating and Graphing Paired-Variable
Statistical Data
kDrawing 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.
Press ior !i(QUIT) to return to the statistical data list.