Graphing of Data

• Why do we display data with graphs?

• Bozeman – Beginners to Graphing 10 min.• http://www.youtube.com/watch?v=9BkbYeTC6Mo&list=PLllV

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• Bozeman Graphing by hand instructions 6 min.• http://www.youtube.com/watch?v=GUYRMdcEs00&list=PLllV

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• Bozeman Graphing Excel Spreadsheet 5 min.• http://www.youtube.com/watch?v=yvYvHU83_6Y&list=PLllVw

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• Visualize data• See relationship btw variables.• See outliers from data.• Show math relationship.• Finding physical constants.• We use line graphs.

Give graphical data display because:

Types of graphs

• We usually use line graphs to find relationship between variables.

Graph Analysis• Direct Linear proportion y = mx + b.• If y is proportional to x, the graph of y vs. x is a straight line passing

through the origin.• Double x, y double, triple x, y triples etc.• Since slope is constant, y/x = k any 2 points on the line.

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• What graph is this?• Y = -kx.• This is a linear graph!• Is it proportional?

Inverse hyperbolic• Y = k/x yx = k• We make transformation of graph to line by calculating

& plotting the function x on the x axis.• Linearize graph by plotting y against 1/x to get linear.

What would the transformed graph look like?

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Slope will be k

Parabolic

• Y = kx2. y/x2 = k• Transform graph y against x2 make it linear• What will the slope be?

Cyclic Graph

Sketching graphs

• Graph axis independent (x) / dependent (y). Time goes on x.

• Scale – large take up most of sheet.• Plot dot for average values.• Line or curve of best fit by hand. Can buy shape to

help fit curves. Best fit straight line may or may not pass through origin.

• Linearize Curves.• Calculate slope to find physical constants.