Applications-of-GeoGebra/C3/Statistics-using-GeoGebra/English - Revision history

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Madhurig at 12:53, 16 January 2019

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Vidhya: Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this '''tutorial''' on '''Statistics using GeoGebra''' |-..."

2018-10-30T06:55:25Z

Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this '''tutorial''' on '''Statistics using GeoGebra''' |-..."

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{|border=1
| | '''Visual Cue'''
| | '''Narration'''

|-
| | '''Slide Number 1'''

'''Title Slide'''
| | Welcome to this '''tutorial''' on '''Statistics using GeoGebra'''
|-
| | '''Slide Number 2'''

'''Learning Objectives'''
| | In this '''tutorial''', we will learn how to use '''GeoGebra''' to perform:

'''One Variable Analysis''' to calculate different statistical parameters

'''Two Variable Regression Analysis''' to estimate best fit line

'''Multiple Variable Analysis''' to calculate different statistical parameters
|-
| | '''Slide Number 3'''

'''System Requirement'''
| | Here I am using:

'''Ubuntu Linux '''OS version 16.04

'''GeoGebra''' 5.0.481.0-d
|-
| | '''Slide Number 4'''

'''Pre-requisites'''
| | To follow this '''tutorial''', you should be familiar with:

'''GeoGebra''' interface

Statistics
|-
| | '''Slide Number 5'''

'''Statistics'''

Data analysis and interpretation

'''Measures of central tendency'''

'''Measures of Dispersion'''

Comparing '''variability '''of data series

'''Additional material '''
| |

'''Statistics'''

Statistics deals with

Data analysis and interpretation

Measures of '''central tendency'''

Measures of '''Dispersion'''

Comparing '''variability''' of data series

Please refer to '''additional material''' provided along with this '''tutorial'''.
|-
| | '''Slide Number 6'''

'''Measures of central tendency'''

'''Arithmetic mean '''

'''Median'''

'''Mode'''
| |

'''Measures of central tendency'''

Measures of '''central tendency''' include '''arithmetic mean, median''' and '''mode'''.

They give an idea about centering of data points.
|-
| | '''Slide Number 7'''

'''Measures of Dispersion'''

'''Range'''

'''Quartiles'''

'''Mean'''

'''Standard Deviation (σ) = sqrt (variance)'''
| |

'''Measures of Dispersion''' include '''Range, Quartiles, Mean''' and '''Standard Deviation'''.

'''Range''' is the difference between the highest and lowest data points.

'''Quartiles''' are the data points that divide the list into quarters

'''Mean''' is the sum of all data points divided by the number of points.

'''Standard deviation, sigma''', is the '''squareroot''' of '''variance'''.
It describes how spread out the data are.
|-
| | '''Slide Number 8'''

'''Fish Feed '''

A fishery is testing four feed formulations on its fish: '''A, B, C''' and '''D'''

Length (mm)

Weight (lbs)

Girth (mm)

| | '''Fish Feed '''

Let us look at an example.

A fishery is testing four types of feed formulations on its fish: '''A, B, C''' and '''D'''.

Data to be collected after feeding the fish for 6 months are:

Length in millimeters

Weight in pounds

Girth in millimeters

Let us look at some of these data.
|-
| | '''Slide Number 9'''

'''Fish Feed Data'''

[[Image:]]
| | We will use these data for our '''analyses'''.

Please download the '''code file''', '''Fishery-data''', provided along with this '''tutorial'''.
|-
| | '''Slide Number 10'''

'''Box Plot'''

[[Image:]]
| | '''Box Plot'''

'''Box plot''' is a standardized way of showing data, based on the '''five number summary'''.

'''Minimum''' and '''maximum''' values are the '''whiskers''' of the '''box plot'''.

The '''box''' spans first to third '''quartiles'''.

The segment inside the box shows the '''median'''.
|-
| | Show the '''GeoGebra''' window.
| | I have opened the '''GeoGebra''' interface.
|-
| | Click on '''View''' tool and select '''Spreadsheet'''.
| | Click on '''View''' tool and select '''Spreadsheet'''.
|-
| | Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.
| | Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.

This will close these views.
|-
| | In the '''code file''', drag '''mouse''' to highlight length and weight data from '''columns H''' and '''I'''.

Show data in '''columns H''' and '''I'''.

Press '''Ctrl''' key down and press '''C'''.
| | In the '''code file''', drag '''mouse''' to highlight length and weight data from '''columns H''' and '''I'''.

These are data for fish that have been fed formulation '''C'''.

Hold '''Control''' key down and press '''C'''.
|-
| | Click on '''Spreadsheet''' view in '''GeoGebra'''.
| | Click in the top of the '''Spreadsheet''' in '''GeoGebra'''.
|-
| | Press '''Ctrl''' key down and press '''V'''.
| | Hold '''Control''' key down and press '''V'''.

This will copy and paste the highlighted data from the '''code file''' into '''GeoGebra'''.
|-
| | Place the '''cursor''' on the first column header in '''Spreadsheet''' view.

Drag and adjust '''column A''''s width.
| | Place the '''cursor''' on the first column header in '''Spreadsheet''' view.

Drag and adjust '''column A''''s width.
|-
| | Right-click on '''column A''' heading of '''Length (mm)'''.

Select '''Object Properties'''.

Point to '''dialog box'''.
| | Right-click on '''column A''' heading of '''Length millimetres'''.

Select '''Object Properties'''.

A '''dialog box''' opens.
|-
| | Click on '''Text tab''' and change the name to '''Length (mm)-C'''.

Close the '''dialog box'''.

Similarly, add '''–C''' to '''Weight (lbs)'''.
| | Click on '''Text tab''' and change the name to '''Length millimetres''' hyphen '''C'''.

Close the '''dialog box'''.

Similarly, add '''hyphen C''' to '''Weight pounds'''.
|-
| | Adjust '''column B''' width.
| | Adjust '''column B''' width.
|-
| | Use '''mouse''' to drag and highlight first '''column A'''’s length data and label in '''GeoGebra'''.
| | Click on '''column A''' heading of '''Length millimetres C'''.

Drag to highlight length data in '''Spreadsheet''' view.
|-
| | Below the '''menubar''', click on '''One Variable Analysis''' tool.

Point to '''Data Source''' popup window.

Click on '''Analyze button'''.
| | Below the '''menubar''', click on '''One Variable Analysis''' tool.

A '''Data Source''' popup window appears.

Click on '''Analyze button'''.
|-
| | Point to '''Data Analysis''' window and '''histogram'''.
| | A '''Data Analysis''' window appears.

By default, a '''histogram''' is plotted.
|-
| | Drag the boundary to see the graph properly.
| | Drag the boundary to see the graph properly.
|-
| | Point to length on the '''x-axis''' and frequency on the '''y-axis'''.
| | The length is plotted on the '''x-axis'''.

The number of fish that are of a particular length, the '''frequency''', is plotted on the '''y-axis'''.
|-
| | Point to the '''display box''' above the graph containing the word '''Histogram'''.
| | Note the '''display box''' above the graph containing the word '''Histogram'''.
|-
| | In the '''display box''', click on the '''dropdown menu button'''.
| | In the '''display box''', click on the '''dropdown menu button''' to display the list of plots.
|-
| | Select different options ('''Bar chart, box plot''' etc) and see how they look.
| | Select different plot options ('''Bar chart, box plot''' etc) and observe the plots.
|-
| | Select '''Histogram'''.

Point to '''slider''' to the right of the display.
| | We will stay with the '''histogram''' option.

To the right of the '''dropdown menu''' is a '''slider'''.
|-
| | Drag the '''slider''' from left to right to go to 20.
| | Drag the '''slider''' from left to right to go to 20.
|-
| | Point to rectangles between minimum and maximum values of data.
| | The '''slider''' changes the number of rectangles between the minimum and maximum values of data.
|-
| | Click on '''Options''' button to the right of the '''slider'''.
| | Click on '''Options''' button to the right of the '''slider'''.
|-
| | Under '''Classes''', check '''Set Classes Manually'''.
| | Under '''Classes''', check '''Set Classes Manually check box'''.

This displays '''Start''' and '''Width text-boxes''' to the left of the '''Options button'''.
|-
| | Type 800 in the '''Start text-box''' and press '''Enter'''.

Show the value of 5 in the '''Width text-box'''.
| | As all the fish are over 800 mm long, type 800 in the '''Start text-box''' and press '''Enter'''.

We will stay with the default value of 5 for rectangle '''width'''.
|-
| | Uncheck '''Set Classes Manually'''.
| | Uncheck '''Set Classes Manually''' check box.
|-
| | Click on '''Options button''' again to hide the window.
| | Click on '''Options button''' again to hide the window.
|-
| | Click on '''Show Data''' tool >> point to data highlighted in the '''Spreadsheet'''.
| | Above the '''Histogram text-box''', click on the third '''Show Data tool button'''.

This displays all the data highlighted in the '''Spreadsheet'''.
|-
| | Drag the boundary to see the data properly.
| | Drag the boundary to see the data properly.
|-
| | Click on '''Show Data''' tool again to hide the list.
| | Click on the '''Show Data''' tool again to hide the list.
|-
| | Click on '''Show 2nd Plot''' tool.
| | Above the '''Histogram text-box''', click on the last '''Show 2nd Plot tool button'''.
|-
| | Select '''histogram''' for top plot and '''box plot''' for bottom plot.
| | The same data are graphed in two vertically placed plots.

You can select plot types from the '''dropdown menu''' above each plot.
|-
| | Click on '''Show Statistics''' tool.

Point to '''Statistics''' for both plots.
| | Above the '''Histogram text-box''', click on the second '''Show Statistics tool button'''.

'''Statistics''' for the plot appears as a '''panel''' in the middle.
|-
| | Drag the boundary to see it properly.
| | Drag the boundary to see it properly.
|-
| | Click and point to '''Median''', '''Min''', '''Max''', '''Q1''' and '''Q3''' values in the '''box plot'''.
| | Let us compare '''histogram''' and '''box plot'''.

In the '''box plot''', locate the '''Median''', '''Min''', '''Max''', '''Q1''' and '''Q3''' values.
|-
| | Click on the button next to '''Options button''' above the plot.
| | Above each plot, in the upper right corner, click on the '''button''' next to '''Options'''.

A '''dropdown menu''' appears with which you can copy each plot to '''Clipboard''' or '''export''' it as an '''image'''.
|-
| | Click on '''Show Statistics tool button''' to hide the data.
| | Click on '''Show Statistics tool button''' to hide the data.
|-
| | Close the '''Data Analysis''' window.
| | Close the '''Data Analysis''' window.
|-
| | '''Slide Number 11'''

'''Least Squares Linear Regression (LSLR)'''

Changing an independent variable '''x''' changes the dependent variable '''y'''.

'''LSLR''' predicts '''y''' based on '''x''' value.

'''LSRL (best fit line) y = b0 + b1x'''

'''Coefficient of determination R2'''
| | '''Least Squares Linear Regression (LSLR)'''

Changing an independent variable '''x''' changes the dependent variable '''y'''.

'''LSLR''' predicts '''y''' based on '''x''' value.

'''Least Squares Regression Line (LSRL)''' is also called the '''best fit line'''.

It is given by '''y = b0 + b1x'''.

'''b0''', the '''y intercept''', is a '''constant'''.

'''b1''', the '''slope''', is the '''regression coefficient'''.

'''Coefficient of determination R squared'''

'''R squared''' ranges from 0 to 1.
|-
| | Show length and weight data in the '''Spreadsheet''' in the '''GeoGebra'''.
| | Let’s go back to the length and weight data in the '''Spreadsheet''' view in '''GeoGebra'''.
|-
| | Drag '''mouse''' to highlight all labels and data in the two '''columns'''.
| | Drag and select all the data in both '''columns'''.
|-
| | Under '''One Variable Analysis''', click on '''Two Variable Regression Analysis''' tool.
| | Under '''One Variable Analysis''', click on '''Two Variable Regression Analysis''' tool.
|-
| | Click '''Analyze button''' in the '''Data Source window''' that pops up.
| | In the '''Data Source window''' that pops up, click '''Analyze button'''.
|-
| | '''Data Analysis''' window appears.
| | A '''Data Analysis''' window appears with two plots.
|-
| | Show both plots.
| | By default, the upper plot is a '''Scatterplot''' and the lower a '''Residual plot'''.
|-
| | Click on '''Show Statistics''' tool to see '''Statistics'''.
| | Click on '''Show Statistics''' tool to see the '''Statistics'''.
|-
| | Drag the boundary to see them properly.
| | Drag the boundary to see them properly.
|-
| | Below '''Statistics window''', click on the '''Regression Model menu button''' and select '''Linear'''.
| | Below the '''Statistics window''', click on the '''Regression Model menu button''' and select '''Linear'''.
|-
| | Point to the red line that is drawn through some points.
| | Note the red line that is drawn through some points in the '''Scatterplot'''.
|-
| | Point to length plotted on '''x-axis''', weight on '''y-axis'''.
| | Length is plotted along '''x-axis''' and weight along '''y-axis'''.
|-
| | Point to equation is given in red, '''y= 0.08x-48.39'''.
| | This is the '''best fit line''' that passes through as many points as possible.

Its equation is given in red, '''y= 0.08x-48.39''', at the bottom.
|-
| | Point to '''R2''' value of 0.7722.
| | Note that '''R squared''' value for this line is 0.7722 in the '''Statistics window.'''

The closer '''R squared '''value is to 1, the better is the prediction of '''y''' from '''x''' by the equation.

This ''' R squared''' value indicates good fit between the model and the actual data.
|-
| | Select other '''regression models''' to see effects on '''R2'''.
| | Select other '''regression models''' to see effects on the '''R squared''' value.
|-
| | Point to the lower '''Residual Plot'''.
| | The lower plot is the '''Residual Plot'''.

It shows '''residuals''' along the '''y-axis''', '''length''' along the '''x-axis'''.

'''Residuals '''are the differences between observed and predicted values of all points.

Absence of '''U''' shape in the '''scatterplot''' means that '''linear regression''' is appropriate for these data.
|-
| | Click on '''Switch Axes button'''.
| | Above the '''Statistics window''', click on the last '''Switch Axes button'''.
|-
| | Point to length now plotted on '''y-axis''' and weight on '''x-axis'''.
| | For the '''scatterplot''', length is now plotted along '''y-axis''' and weight along '''x-axis'''.
|-
| | Point to the '''best fit line''' and '''statistics'''.

Point to equation '''y= 9.91x + 684.3'''.
| | Observe that the '''best fit line''' and many '''statistics''' change.
|-
| | Point to '''r''', '''R2 '''and '''rho (ρ)'''.
| | The only statistics that remain the same are '''r''', '''R squared '''and '''rho (ρ)'''.

Note that '''r''' and '''rho''' are greater than 0.8, indicating positive '''correlation'''.

Weight increases as length increases for fish given '''feed C'''.

The relationship is strong and well predicted by the '''best fit lines'''.
|-
| | Again, click on '''Switch Axes button'''.
| | Again, click on '''Switch Axes button'''.
|-
| | Point to '''Symbolic Evaluation''' at the bottom.
| | At the bottom, in '''Symbolic Evaluation''', you can enter a value for '''x''' to get a prediction for '''y'''.
|-
| | Point at the line in the '''Scatterplot'''.
| | If you choose '''x''' values below the '''x-intercept''' of the line, you will get negative values of '''y'''.

To get logical predictions, we will enter '''x''' values above the '''x-intercept'''.
|-
| | In '''Symbolic Evaluation''', type in a value for '''x''' and press '''Enter'''.
| | In '''Symbolic Evaluation''', in the text-box for '''x''', type 800 and press '''Enter'''.
|-
| | Point to '''y''' value appearing next to the '''display box'''.
| | Note that a '''y''' value appears next to the '''display box'''.

The '''x''' value was substituted in the '''best fit line''' equation to get the '''y''' value.
|-
| | Again, click on '''Show Statistics tool button'''.
| | Again, click on '''Show Statistics tool button'''.
|-
| | Close the '''Data Analysis window'''.
| | Close the '''Data Analysis window'''.
|-
| | Point to length and weight data in the '''Spreadsheet'''.
| | Let’s go back to the length and weight data in the '''Spreadsheet'''.
|-
| | Drag '''mouse''' to highlight all labels and data in the two '''columns'''.
| | In the '''Spreadsheet''', select all the data in both '''columns'''.
|-
| | Under '''One Variable Analysis''', click on '''Multiple Variable Analysis''' tool.
| | Under '''One Variable Analysis''', click on '''Multiple Variable Analysis''' tool.
|-
| | Click '''Analyze button''' in the '''Data Source window''' that pops up.
| | In the '''Data Source window''' that pops up, click '''Analyze button'''.
|-
| | Point to''' Stacked Box Plots''' in the window and to the cell numbers in each row.
| | '''Stacked Box Plots''' appear in the window.

They are for length and weight data.
|-
| | Click on '''Show Statistics''' tool.

Point to '''Statistics''' for both plots.
| | Above the plot, click on the second '''Show Statistics''' tool.

'''Statistics''' for both plots appear below.
|-
| | Place the '''cursor''' on the boundary between the plot and statistics.

When the arrow appears, drag the boundary to resize the windows.
| | Place the '''cursor''' on the boundary between the plot and statistics.

When the '''arrow''' appears, drag the boundary to resize the windows.
|-
| | Close '''Data Analysis window'''.
| | Close '''Data Analysis window'''.
|-
| |
| | Let us summarize.
|-
| | '''Slide Number 12'''

'''Summary'''
| | In this '''tutorial''', we have learnt how to use '''GeoGebra''' to perform:

'''One Variable Analysis''' to calculate different statistical parameters

'''Two Variable Regression Analysis''' to estimate best fit line

'''Multiple Variable Analysis''' to calculate different statistical parameters
|-
| | '''Slide Number 13'''

'''Assignment'''
| | '''Assignment'''

Perform statistical analyses for weight and girth data given in this '''tutorial'''

Four oils were used to deep fry chips. Six chips were chosen from each batch fried in a given oil. Amount of absorbed fat was measured for these chips Is any of the oils absorbed more than the others?

[[Image:]]
|-
| | '''Slide Number 14'''

'''About Spoken Tutorial project'''
| | The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
|-
| | '''Slide Number 15'''

'''Spoken Tutorial workshops'''
| | The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
|-
| | '''Slide Number 16'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them
| | Please post your timed queries on this forum.
|-
| | '''Slide Number 17'''

'''Acknowledgement'''
| | '''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
|-
| |
| | This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}

@@ Line 9: / Line 9: @@
 '''Title Slide'''
-|| Welcome to this '''tutorial''' on '''Statistics using GeoGebra'''
+|| Welcome to this '''tutorial''' on '''Statistics using GeoGebra'''.
 |-
 || '''Slide Number 2'''
@@ Line 16: / Line 16: @@
 || In this '''tutorial''', we will learn how to use '''GeoGebra''' to perform:
-'''One Variable Analysis''' to calculate different statistical parameters
+'''One Variable Analysis''' to calculate different statistical parameters.
-'''Two Variable Regression Analysis''' to estimate best fit line
+'''Two Variable Regression Analysis''' to estimate best fit line.
-'''Multiple Variable Analysis''' to calculate different statistical parameters
+'''Multiple Variable Analysis''' to calculate different statistical parameters.
 |-
 || '''Slide Number 3'''
@@ Line 27: / Line 27: @@
 || Here I am using:
-'''Ubuntu Linux '''Operating System version 16.04
+'''Ubuntu Linux '''Operating System version 16.04.
-'''GeoGebra''' 5.0.481.0-d
+'''GeoGebra''' 5.0.481.0-d.
 |-
 || '''Slide Number 4'''
@@ Line 36: / Line 36: @@
 || To follow this '''tutorial''', you should be familiar with:
-'''GeoGebra''' interface
+'''GeoGebra''' interface.
 Statistics
@@ Line 44: / Line 44: @@
 '''Statistics'''
-Data analysis and interpretation
+Data analysis and interpretation.
 '''Measures of central tendency'''
-'''Measures of Dispersion'''
+'''Measures of Dispersion'''.
 Comparing '''variability '''of data series
@@ Line 55: / Line 55: @@
 ||Statistics deals with
-Data analysis and interpretation
+Data analysis and interpretation.
-Measures of '''central tendency'''
+Measures of '''central tendency'''.
-Measures of '''Dispersion'''
+Measures of '''Dispersion'''.
-Comparing '''variability''' of data series
+Comparing '''variability''' of data series.
 Please refer to '''additional material''' provided along with this '''tutorial'''.
@@ Line 85: / Line 85: @@
 Data to be collected after feeding the fish for 6 months are:
-Length in millimeters
+Length in millimeters.
-Weight in pounds
+Weight in pounds.
-Girth in millimeters
+Girth in millimeters.
 Let us look at some of these data.
@@ Line 97: / Line 97: @@
 '''Fish Feed Data'''
-|| We will use these data for our '''analyses'''.
+||'''Fish Feed Data'''
 Please download the '''code file''', '''Fishery-data''', provided along with this '''tutorial'''.
@@ Line 468: / Line 470: @@
 || In this '''tutorial''', we have learnt how to use '''GeoGebra''' to perform:
-'''One Variable Analysis''' to calculate different statistical parameters
+'''One Variable Analysis''' to calculate different statistical parameters.
-'''Two Variable Regression Analysis''' to estimate best fit line
+'''Two Variable Regression Analysis''' to estimate best fit line.
-'''Multiple Variable Analysis''' to calculate different statistical parameters
+'''Multiple Variable Analysis''' to calculate different statistical parameters.
 |-
 || '''Slide Number 11'''
@@ Line 478: / Line 480: @@
 '''Assignment'''
-Perform statistical analyses for weight and girth data
+Perform statistical analyses for weight and girth data.
 Is any of the oils absorbed more than the others?
@@ Line 484: / Line 486: @@
 || '''Assignment'''
-Perform statistical analyses for weight and girth data given in this '''tutorial'''
+Perform statistical analyses for weight and girth data given in this '''tutorial'''.
 Four oils were used to deep fry chips.

@@ Line 486: / Line 486: @@
 Perform statistical analyses for weight and girth data given in this '''tutorial'''
-Four oils were used to deep fry chips.  Amount of absorbed fat was measured for 6 chips fried in 4 oils.  Is any of the oils absorbed more than the others?
+Four oils were used to deep fry chips.
 |-
 || '''Slide Number 12'''