Kaitlyn Stallings - R5
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University of Texas *
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Course
1315
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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4
Uploaded by PrivateAtomWolverine15
Recitation: Submit this worksheet Name: Kaitlyn Stallings
Recitation (R5): Graphing and Analysis: Worksheet
Exercise 1: Using the graph of mass and volume (Sheet 1 of the excel sheet) and the best fit line equation, answer the following on this worksheet: Please attach your graph for Sheet 1 here (copy and paste from excel)
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f(x) = 8.94 x − 1.78
R² = 1
Plot of Volume vs Mass
Mass (g)
Linear (Mass (g))
Volume (cm^3)
Mass (g)
Figure 1. Plot of volume vs mass gives us the linear trend as the volume increases, the mass also increases
with the slope of 8.94 g/cm3.
a.
In a visual inspection of the line and data, how confident are you in your ability to make predictions from this data? Explain how you reached this conclusion in a complete sentence. This data is very clear and precise, so it’s very easy to interpret and predict. It follows a linear path, so it’s easy to plug in different volumes into the equation to calculate the future mass. The line is visually linear and continuously increasing. To reach this conclusion, I plotted the given data points and established the line’s equation.
b.
Given your graph, identify what mass you would expect if the volume is 200 cm
3
? (Extrapolate the line to make this prediction.)
1786.4046 grams 1
Recitation: Submit this worksheet Name: Kaitlyn Stallings
c.
What is the density of this metal? (Density is the slope of the line.)
The density of the metal is 8.94 g/cm3.
d.
Consider the error associated with the data point (165, 1473), the highest data point on the graph. What is the range* of ‘acceptable’ values for the volume and for the mass if you were to do the experiment again?
i.
Volume = The range of acceptable values would be 156.75-173.25 cm3
ii.
Mass = The range of acceptable values would be 1,399.35-1,546.65 grams
*Range includes lowest to highest values. For example, if the value is 10.0 cm and acceptable error is 5%, then 9.5-10.5 cm would be the range.
Exercise 2: S
ubmit your properly labeled graph
of mass v. heat (Sheet 2 of your excel spreadsheet) and answer accompanying questions.
I. Label the graph with a Title and the axes names, including the units. Be sure to include the error bars. Insert (copy and paste from excel) here:
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Recitation: Submit this worksheet Name: Kaitlyn Stallings
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f(x) = 711.95 x − 809.08
R² = 0.71
Plot of Mass of KOH vs Heat
Mass of KOH (g)
Heat (J)
Figure 2. Mass of KOH vs Heat displays the relationship between the two units with the slope of 711.95 J/g.
II. Using the graph and the best fit line equation, answer the following on this worksheet, : a.
From a visual inspection: How confident are you in the equation of the line? From a visual inspection, I am not very confident in the equation of the line because it appears to
lack a patterned tendency. The line of best fit is not precise to the points. b.
Would you call this class data precise? Explain
I would not consider this data to be precise, you can visualize that the points are relatively to the trendline but not directly on it.
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Recitation: Submit this worksheet Name: Kaitlyn Stallings
c.
Do you know whether the line and the equation of the line are accurate representations? The points on the graph are relative to the line and we can use this observation to assume accuracy. We can also use this assumption with the equation of the line. d.
Do you think the error bars generated by Excel represent the precision or the accuracy?
The error bars represent the accuracy because they signify the margin of error, indicating that the
data is not precise. Having a smaller margin of error indicates the data is more precise. 4