Topic 11.2: Measurement and Data Processing Graphing

11.2 Graphing EI: Graphs are a visual representation of trends in data. NOS: The idea of correlation – can be tested in experiments whose results can be displayed graphically.

U 1. Graphical Techniques Why do are graphs used? Graphs are an effective means of communicating the effect of the independent variable on a dependent variable, and can lead to determination of physical quantities.

U1. Graphical Techniques Graphs are used to present and analyze data. – show the relationship between the independent variable and the dependent variable Independent Dependent Example Graph

U2. Sketched graphs Sketched graphs: – Have labeled, but unscaled axes – Used to show qualitative trends Variables that are proportional or inversely proportional Independent Dependent Example Graph

U3. Drawn Graphs Graphs MUST have: A title Label axes with quantities and units Time (min.) Mass (g) Candle Mass After Burning

U3, A &S 1. Drawn Graphs Graphs MUST have: Use available space as effectively as possible Use sensible linear scales- NO uneven jumps Plot ALL points correctly Time (min.) Mass (g) Candle Mass After Burning

A&S 3. Best Fit Lines Best Fit Lines should be – drawn smoothly and clearly – Do not have to go through all the points, but do show the overall trend Time (sec) Temperature ( o C)

A & S 4 Physical quantities from graphs Find the gradient (slope) and the intercept Use y = m x + b for a straight line y= dependent variable x = independent variable m= the gradient (slope) b = the intercept on the vertical (y) axis

A & S 4 Physical quantities from graphs Ex: to find the slope (m), find 2 data points (2,5) and (4, 10) m= (y 2 -y 1 ) = (10-5) = 5 = 2.5 (x 2 -x 1 ) (4-2) 2

A & S 2. Interpretation of Graphs Variables: Independent- the cause, plotted on the horizontal axis (x-axis) AKA: Manipulated Independent Dependent Example Graph

A & S 2 Interpretation of Graphs Variables: Dependent- the effect, plotted on the the vertical axis (y-axis) AKA: Responding Independent Dependent Example Graph

A & S 2. Interpretation of Graphs Interpolation: determining an unknown value using data points within the values already measured

A & S 2. Interpretation of Graphs Extrapolation: when a line has to be extended beyond the range of the measurements of the graph to determine other values – Absolute zero can be found by extrapolating the line to lower temperatures.

Graphing in Excel Enter data into Excel – IV in left column – DV in right column Highlight data with mouse Click on – “Insert” tab – “Scatter with smooth lines & markers”

Graphing in Excel Edit titles under “Chart Tools: Layout” – Graph Title: “IV vs. DV” – IV with units on x-axis – DV with units on y-axis – Change gridlines to your liking Establish Line of Best Fit – Right click on line and “Add Trendline” – Make sure “Linear,” “Automatic” and “Display Equation on Chart” are all checked – Press Close… and voila!!!