Casio CFX-9850G PLUS Manuale utente

Chapter

Statistical Graphs and

Calculations

This chapter describes how to input statistical data into lists, how

to calculate the mean, maximum and other statistical values, how

to perform various statistical tests, how to determine the confi-

dence interval, and how to produce a distribution of statistical

data. 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 Performing Statistical Calculations

18-6 Tests

18-7 Confidence Interval

18-8 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 appears on the screen when you perform a graphing

operation will probably differ somewhat from those shown in this manual.

250

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.

Use

f, c, d

and

to move

the highlighting around the lists.

P. 251 •{GRPH} ... {graph menu}

P. 270 •{CALC} ... {statistical calculation menu}

P. 277 •{TEST} ... {test menu}

P. 294 •{INTR} ... {confidence interval menu}

P. 304 •{DIST} ... {distribution menu}

P. 234 •{SRT·A}/{SRT·D} ... {ascending}/{descending} sort

P. 233 •{DEL}/{DEL·A} ... deletes {highlighted data}/{all data}

P. 234 •{INS} ... {inserts new cell at highlighted cell}

•The procedures you should use for data editing are identical to those you use

P. 229 with the list function. For details, see “17. List Function”.

251

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}

kInputting Data into Lists

Input the two groups of data into List 1 and List 2.

a.fwb.cw

c.ewewf.cw

-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.

kPlotting a Scatter Diagram

Use the data input above to plot a scatter diagram.

1(GRPH)1(GPH1)

•To return to the statistical data list, press Jor !Q.

•View Window 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”.

Note that View Window parameters are set automatically for the following

types of graphs regardless of whether or not the Stat Wind item is set to

“Manual”.

1-Sample ZTest, 2-Sample ZTest, 1-Prop ZTest, 2-Prop ZTest, 1-Sample

tTest, 2-Sample tTest, χ2Test, 2-Sample FTest (x-axis only disregarded).

252

While the statistical data list is on the display, perform the following procedure.

!Z2(Man)

J(Returns to previous menu.)

•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 relationship

become clear, however, when we plot the data on a graph, using one set of

values as x-data and the other set as y-data.

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/ydata is a point on the scatter

diagram.

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.

•{GPH1}/{GPH2}/{GPH3} ... only one graph {1}/{2}/{3} drawing

•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.

P. 252 •{SEL} ... {simultaneous graph (GPH1, GPH2, GPH3) selection}

P. 254 •{SET} ... {graph settings (graph type, list assignments)}

•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).

•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.

1. Graph draw/non-draw status [GRPH]-[SEL]

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 4(SEL) displays the graph On/Off screen.

18 - 2 Paired-Variable Statistical Calculation Examples

253

•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} ... setting {On (draw)}/{Off (non-draw)}

• {DRAW} ... {draws all On graphs}

3. To return to the graph menu, press J.

uTo draw a graph

Example To draw a scatter diagram of Graph 3 only

1(GRPH)4(SEL) 2(Off)

cc1(On)

6(DRAW)

2. 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.

• Mark Type

This setting lets you specify the shape of the plot points on the graph.

Paired-Variable Statistical Calculation Examples 18 - 2

254

uTo display the general graph settings screen [GRPH]-[SET]

Pressing 6(SET) displays the general graph settings screen.

•The settings shown here are examples only. The settings on your general graph

settings screen may differ.

uStatGraph (statistical graph specification)

•{GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3}

uGraph Type (graph type specification)

•{Scat}/{xy}/{NPP} ... {scatter diagram}/{xy line graph}/{normal probability plot}

–––

•{Hist}/{Box}/{Box}/{N·Dis}/{Brkn} ... {histogram}/{med-box graph}/{mean-box

graph}/{normal distribution curve}/{broken 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}/{sine regression graph}/

{logistic regression graph}

uXList (x-axis data list)

•{List1}/{List2}/{List3}/{List4}/{List5}/{List6} ... {List 1}/{List 2}/{List 3}/{List 4}/

{List 5}/{List 6}

uYList (y-axis data list)

•{List1}/{List2}/{List3}/{List4}/{List5}/{List6} ... {List 1}/{List 2}/{List 3}/{List 4}/

{List 5}/{List 6}

uFrequency (number of data items)

•{1} ... {1-to-1 plot}

•{List1}/{List2}/{List3}/{List4}/{List5}/{List6} ... frequency data in {List 1}/

{List 2}/{List 3}/{List 4}/{List 5}/{List 6}

uMark Type (plot mark type)

•{ }/{×}/{•} ... plot points: { }/{×}/{•}

18 - 2 Paired-Variable Statistical Calculation Examples

255

uGraph Color (graph color specification)

•{Blue}/{Orng}/{Grn} ... {blue}/{orange}/{green}

uOutliers (outliers specification)

•{On}/{Off} ... {display}/{do not display} Med-Box outliers

kDrawing an xy Line Graph

P. 254 Paired data items can be used to plot a scatter diagram. A scatter diagram where

(Graph Type) the points are linked is an xy line graph.

(xy)

Press Jor !Q to return to the statistical data list.

kDrawing a Normal Probability Plot

P. 254 Normal probability plot contrasts the cumulative proportion of variables with the

(Graph Type) cumulative proportion of a normal distribution and plots the result. The expected

(NPP) values of the normal distribution are used as the vertical axis, while the observed

values of the variable being tested are on the horizontal axis.

Press Jor !Q to return to the statistical data list.

kSelecting the Regression Type

After you graph paired-variable 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}/{Med}/{X^2}/{X^3}/{X^4}/{Log}/{Exp}/{Pwr}/{Sin}/{Lgst} ... {linear regres-

sion}/{Med-Med}/{quadratic regression}/{cubic regression}/{quartic

regression}/{logarithmic regression}/{exponential regression}/{power

regression}/{sine regression}/{logistic regression} calculation and graphing

•{2VAR} ... {paired-variable statistical results}

Paired-Variable Statistical Calculation Examples 18 - 2

CFX

256

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)

kGraphing Statistical Calculation Results

You can use the parameter calculation result menu to graph the displayed

regression formula.

P. 268 • {COPY} ... {stores the displayed regression formula as a graph function}

• {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).

P. 255 For details on the meanings of function menu items at the bottom of the display, see

“Selecting the Regression Type”.

18 - 2 Paired-Variable Statistical Calculation Examples

257

Calculating and Graphing Single-Variable Statistical Data 18 - 3

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 types of

graphs are available for single-variable statistics.

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

Lists”). Draw the graph using the procedure described under “Changing Graph

Parameters”.

⇒

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.

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 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 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.

P. 251

P. 252

P. 254

(Graph Type)

(Hist)

P. 254

(Graph Type)

(Box)

Q1 Med Q3 maxX

minX

258

To plot the data that falls outside the box, first specify “MedBox” as the graph

type. Then, on the same screen you use to specify the graph type, turn the outliers

item “On”, and draw the graph.

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 population

standard deviation (o– x

n) and above the mean up to the population standard

deviation (o+ x

n). Lines (called whiskers) extend from either end of the box up to

the minimum (minX) and maximum (maxX) 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 mean-box graph.

kNormal Distribution Curve

P. 254 The normal distribution curve is graphed using the following normal distribution

(Graph Type) function.

(N·Dis)

= 1

(2 π)xσ

–2xσ

(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.

18 - 3 Calculating and Graphing Single-Variable Statistical Data

P. 254

(Graph Type)

(Box)

Note :

This function is not usually used in

the classrooms in U.S. Please use

Med-box Graph, instead.

o– x

no o + x

minX

maxX

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