GRAPHING RULES, DATA ANALYSIS SPH3U DAY 3/4 NOTES GRAPHING RULES, DATA ANALYSIS

Variables and Graphing WS Complete both sides – we’ll discuss the rules afterwards!

Graphing Expectations Use a full page of graph paper for graphs in lab reports or assignments. Include the variable and units on each axis (distance (m), time (s), etc.) The title of the graph is in the form of y vs. x (distance versus time, no units needed in title). Calculations are NOT done on the graph, but on a separate page. Errors are indicated by circling dots if no absolute error is known, or error bars for labs.

Graphing Expectations A best fit line or curve is usually expected for all graphs. Slope calculations include units and are rounded based on sig digs (determined by precision of measuring devices in the lab (absolute error)). Use +/- half the smallest division of measuring devices in labs, for precision and to determine how many decimals you must measure to.

Plot distance versus time and distance versus time2. Graph data Plot distance versus time and distance versus time2. time (s)  0.05 s 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00   distance (m)  0.05 m 1.25 2.88 4.05 6.52 9.87 12.57 16.22 20.89 time2 (s)2

Precision This a measurement that has a certain degree of reproducibility. There are a certain number of decimals that everyone agrees to and the last decimal is uncertain – so you can’t have any more decimals!! This error is the +/- lab errors Always determine the +/- error first, before you measure, in a lab.

Accuracy The accuracy of a lab value is found by comparing it to the accepted value found over years of labs and research. Example: Gravity due to the Earth’s field is 9.81 m/s2 and in a lab we may get a value of 9.77 m/s2. This is probably due to lots of experimental errors – not to mention we are at a different altitude here in Ancaster so the gravity is different here (9.81 m/s2 is an average value for the whole planet!) The accuracy formula is accuracy (as a %) = |actual – experimental|/actual x100 Ex) Determine the accuracy based on the above information!

Optional Graph Analysis next slides

Data Analysis Ultimately, we want to find out how the manipulated variable affects the responding variable. All the formulae on your data sheets were found experimentally at some point.

Determining data relationships Once data is plotted, several general shapes may arise: linear, power or inverse (possibly a root curve). If a curve results, we wish to determine the relationship between the variables. Once we get a linear graph, we can determine an equation for the data (and a formula may ensue).

Data Manipulation We can manipulate the graphical data to see what gives a direct relationship. You only manipulate the x-values – Why? If the graph was an inverse curve, you invert the x values and replot. (Plot y vs 1/x) If still not straight you square the inverted values (Plot y vs 1/x2) and so on until a straight line ensues. If a power graph was found first, plot y vs x2, then y vs x3 and so on until a straight line results.

Data Manipulation The equation can be stated once the linear graph is found. Ex) Your plot of d vs t2 gave a straight line, we know that d α t2 and we can add a constant to give an equation. The constant we would put in is the slope of the best-fit straight line. This slope will likely have units, and you would also round your slope to the sig digs of your raw data.