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

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

Example Graph

U3. Drawn Graphs

Graphs MUST have:• A title• Label axes with

quantities and units

Time (min.)

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.)

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)

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= (y2-y1) = (10-5) = 5 = 2.5

(x2-x1) (4-2) 2

A & S 2. Interpretation of Graphs

Variables:Independent- the cause,

plotted on the horizontal axis (x-axis)AKA: Manipulated

Independent

Example Graph

A & S 2 Interpretation of Graphs

Variables:Dependent- the effect,

plotted on the the vertical axis (y-axis)AKA: Responding

Independent

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!!!