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Teacher to ask the students what should they be doing after taking measurements in their investigations.
Promote thinking and discussion
Get the students to sit down with their team mates and verbalise what they are doing with the data collected.
Facilitate Demonstration of Learning
Teacher to guide students to start analysing their data by plotting their raw data into a table with several columns. They should also include columns for treating their data (E.g. Calculating the average and the error). The steps are given in SECTION A below.
After preparing their table of values, the students should be directed to the Logger Pro 3 or other softwares to plot their graphs. Refer to SECTION B below for the steps.
Monitor and provide feedback
Teacher to provide feedback to the students as they provide the evidences of their tables and graphs/histograms/pie charts. Face-to-face consultation may be needed for different groups.
SECTION A: Taking averages, standard deviation and error bars
Scenario:
Students have obtained the data and keyed them in the cells B2, C2, and D2 as the 3 measurements taken. He wanted to calculate the average, the standard error, and the error in his measurements using google spreadsheets.
Solution:
In google spreadsheets, it can be calculated using the following formulas:
D2: =AVERAGE(B2:C2)
E2: =STDEV(B2:C2)/SQRT(N-1)
where N is the number of readings taken. In the example above, the N = 2.
The above statements mean that
D2 will give the average of the 2 entries keyed into B2 and C2.
E2 will give the error, where the standard deviation of the 2 entries keyed into B2 to C2 is divided by the square root of the number of samples (2 samples in this case).
Repeat the process for other values placed in the cells B3, C3, and so on.
You can just copy the formula in the cells in D2 and E2 to the other sets of data.
Note that the average reading should be expressed to the same number of significant figures as the raw data.
Also, the error should be expressed to 1 significant figure. It should also have the same decimal places as the raw data.
The rounded off values are written in the table below.
References
Biology for live (2022). Interpreting error bars. Retrieved from https://www.biologyforlife.com/interpreting-error-bars.html
SECTION B: Graph plotting
There are several softwares that are possible to carry out graph plotting and analysis:
Logger Pro 3 (Recommended for scatter graphs). LINK
Do refer to the help functions within each software or google for instructions on how to carry out the relevant tasks.
Students are reminded that the approach to be taken is heavily dependent on their experimental design. They are advised to plot scatter graphs, histograms or pie charts depending on the type of research that they are carrying out.
Your teacher will provide the necessary guidance based on your project.
SECTION C: Error Bar plotting and Curve fitting (If applicable)
The error bars can be calculated above and plotted as follows:
In Logger Pro3, you should have 1 column for X, f(x), and ERROR.
Click on f(X) column and right click column options, choose f(X).
In the Manual Column Options, choose Error Bar Calculations and Use column --> Error. Click Done and you should get the error bars plotted over the plotted point.
To plot the trend line, you should have some idea what is the expected trend line based on your hypothesis. There are 2 main fitting routines: Linear and Curve fitting.
If you choose curve fit, select the appropriate function or you can define your own function based on your research. Once done, click Try Fit followed by OK.
The trend line will be displayed with the constants A, B, C, D, E, ... indicated together with the equation that you have chosen.
After you have completed your data analysis, do submit your log book to your teacher for feedback.
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