The Cycle of Proof: Dealing with Data. Dealing with Data: Daily Learning Goal The student will be able to compile and interpret data using appropriate.

The Cycle of Proof: The Cycle of Proof: Dealing with DataDealing with Data

The Cycle of Proof: The Cycle of Proof: Dealing with DataDealing with Data

Dealing with Data:Dealing with Data:Daily Learning GoalDaily Learning Goal

The student will be able to compile The student will be able to compile and interpret data using appropriate and interpret data using appropriate formats, including tables and formats, including tables and graphs. (A1.6)graphs. (A1.6)

Qualitative vs. Qualitative vs. QuantitativeQuantitative

QualitativeQualitative observations are observations are descriptive: descriptive:

e.g., “The amplitude of the pendulum e.g., “The amplitude of the pendulum decreased slowly over 10 swings.”decreased slowly over 10 swings.”

QuantitativeQuantitative observations contain observations contain numerical measurements: numerical measurements:

e.g., “The mass of the pendulum was e.g., “The mass of the pendulum was 150 g.”150 g.”

Qualitative DataQualitative Data

Qualitative data should still be Qualitative data should still be specific and exact.specific and exact.

e.g.,e.g., Do NOT say “the solution bubbled Do NOT say “the solution bubbled

and fizzed;” say “a gas was and fizzed;” say “a gas was produced.”produced.”

Do NOT say “the solution got Do NOT say “the solution got cloudy with chunky bits;” say “a cloudy with chunky bits;” say “a precipitate formed.”precipitate formed.”

Quantitative DataQuantitative Data

Quantitative data should contain all Quantitative data should contain all the digits that were measured.the digits that were measured.

E.g., if a length is measured to the E.g., if a length is measured to the nearest millimetre, the nearest nearest millimetre, the nearest millimetre needs to be recorded:millimetre needs to be recorded:

10.0 cm should NOT be recorded as 10.0 cm should NOT be recorded as 10 cm. That .0 was measured!10 cm. That .0 was measured!

TablesTables

Both qualitative and quantitative data Both qualitative and quantitative data can be recorded and presented in can be recorded and presented in tables.tables.

e.g.e.g.

TablesTables

Guidelines for creating tables:Guidelines for creating tables:

Tables are numbered in the order in Tables are numbered in the order in which they appear in the experiment.which they appear in the experiment.

A title explains in detail what information A title explains in detail what information is presented in the table.is presented in the table.

TablesTablesGuidelines for creating tables:Guidelines for creating tables:

Tables are numbered in the order in which Tables are numbered in the order in which they appear in the experiment.they appear in the experiment.

A title explains in detail what information A title explains in detail what information is presented in the table.is presented in the table.

The table is divided into columns and rows The table is divided into columns and rows outlined by solid, ruler-drawn borders.outlined by solid, ruler-drawn borders.

The rows and/or columns have identifying The rows and/or columns have identifying headings.headings.

The units used in the table are shown in The units used in the table are shown in the headings.the headings.

UnitsUnits

Never forget your Never forget your units!units!

Units are important. . . .Units are important. . . .

Units are ImportantUnits are Important

Units are ImportantUnits are Important

Units are ImportantUnits are Important

Units are ImportantUnits are Important

GraphsGraphs

Quantitative data may be presented Quantitative data may be presented and analysed using graphs.and analysed using graphs.

E.g., E.g., Graph 1: Distance-time information for a cart Graph 1: Distance-time information for a cart travelling along a tracktravelling along a track

GraphsGraphsGuidelines for creating graphs:Guidelines for creating graphs:

Graphs are also numbered and titled.Graphs are also numbered and titled.

GraphsGraphsGuidelines for creating graphs:Guidelines for creating graphs:

Graphs are also numbered and titled.Graphs are also numbered and titled. A graph takes up at least ½ a page and A graph takes up at least ½ a page and

preferably an entire page. The horizontal preferably an entire page. The horizontal and vertical ruler-drawn axes should be and vertical ruler-drawn axes should be placed approximately 2 cm from the edge placed approximately 2 cm from the edge of the page.of the page.

GraphsGraphsGuidelines for creating graphs:Guidelines for creating graphs:

Graphs are also numbered and titled.Graphs are also numbered and titled. A graph takes up at least ½ a page and A graph takes up at least ½ a page and

preferably an entire page. The horizontal and preferably an entire page. The horizontal and vertical ruler-drawn axes should be placed vertical ruler-drawn axes should be placed approximately 2 cm from the edge of the approximately 2 cm from the edge of the page.page.

The axes are labeled with the variables The axes are labeled with the variables (including units). (including units). Unless otherwise directedUnless otherwise directed, , the independent variable is placed on the the independent variable is placed on the horizontal axis and the dependent variable horizontal axis and the dependent variable on the vertical axis.on the vertical axis.

GraphsGraphsMore guidelines for creating graphs:More guidelines for creating graphs:

The scale is chosen so that all of the The scale is chosen so that all of the points plotted fit on the graph and take up points plotted fit on the graph and take up as much space as possible on the graph. as much space as possible on the graph. The increments of the scale should be in The increments of the scale should be in multiples of 1, 2, or 5.multiples of 1, 2, or 5.

GraphsGraphsMore guidelines for creating graphs:More guidelines for creating graphs:

The scale is chosen so that all of the The scale is chosen so that all of the points plotted fit on the graph and take up points plotted fit on the graph and take up as much space as possible on the graph. as much space as possible on the graph. The increments of the scale should be in The increments of the scale should be in multiples of 1, 2, or 5.multiples of 1, 2, or 5.

The points are plotted in pencil with a The points are plotted in pencil with a circle surrounding each sharp dot. A circle surrounding each sharp dot. A ruler-drawn line of best fit (or if ruler-drawn line of best fit (or if appropriate, a curve of best fit) is drawn appropriate, a curve of best fit) is drawn through the points.through the points.

The Line/Curve of Best The Line/Curve of Best FitFit

Remember that a line of best fit should Remember that a line of best fit should have as many points above the line as have as many points above the line as below the line and that the below the line and that the displacements between the points and displacements between the points and the line should not form a trend (i.e. all the line should not form a trend (i.e. all points below the line should not be the points below the line should not be the points to the left and all points above the points to the left and all points above the line should not be the points to the line should not be the points to the right).right).

The Line/Curve of Best The Line/Curve of Best FitFit

Remember that a line of best fit should have Remember that a line of best fit should have as many points above the line as below the as many points above the line as below the line and that the displacements between line and that the displacements between the points and the line should not form a the points and the line should not form a trend (i.e. all points below the line should trend (i.e. all points below the line should not be the points to the left and all points not be the points to the left and all points above the line should not be the points to above the line should not be the points to the right). the right).

If (0, 0) is a known data point, use that If (0, 0) is a known data point, use that information when drawing the line. information when drawing the line.

Note also that the line should extend beyond Note also that the line should extend beyond the points to allow for extrapolation.the points to allow for extrapolation.

Trends in GraphsTrends in Graphs

After the data is graphed, the trend in After the data is graphed, the trend in the data may be analysed.the data may be analysed.

Linear IncreaseLinear Increase

This graph shows a linear increase: This graph shows a linear increase:

as the independent variable increases, as the independent variable increases, the dependent variable increases the dependent variable increases linearly.linearly.

Linear DecreaseLinear Decrease

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable decreases linearly.decreases linearly.

Increase at an increasing Increase at an increasing raterate

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable increases at an increasing rate.increases at an increasing rate.

Increase at an increasing Increase at an increasing raterate

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable increases at an increasing rate.increases at an increasing rate.

This is not necessarily an exponential This is not necessarily an exponential increase. It could be a quadratic increase. It could be a quadratic increase. The two are not the same increase. The two are not the same thing!thing!

Increase at an Increase at an decreasing ratedecreasing rate

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable increases at an decreasing rate.increases at an decreasing rate.

Decrease at an Decrease at an increasing rateincreasing rate

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable decreases at an increasing rate.decreases at an increasing rate.

Decrease at an Decrease at an decreasing ratedecreasing rate

Here, as the independent variable Here, as the independent variable increases, the dependent variable increases, the dependent variable decreases at an decreasing rate.decreases at an decreasing rate.

No RelationshipNo Relationship

This graph shows NO RELATIONSHIP This graph shows NO RELATIONSHIP between the independent and between the independent and dependent variables.dependent variables.

Observations vs. Observations vs. ConclusionsConclusions

Statements like “as the independent Statements like “as the independent variable increases, the dependent variable increases, the dependent variable increases linearly,” are variable increases linearly,” are conclusionsconclusions, not observations, and , not observations, and appear in the Discussion or the appear in the Discussion or the Conclusion section(s).Conclusion section(s).