Lab_Report_Intro_to_Graphing Barb (1)
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Pueblo Community College *
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Course
1111C43
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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7
Uploaded by DrQuetzal4128
Introduction to Graphing
Student Name
Barbara Louzada Grady
Date
February 12, 2024
1
Instructions: 1.
Please read all of the introduction and background information within the investigative manual. a.
Once you have done so answer the prelab question BEFORE completing any of the lab’s activities. 2.
Once you have completed the prelab questions proceed to the activities of the lab within the investigative manual. a.
As you read through the instructions for completing each activity
make sure you also:
i.
Complete any instructions (append photos, etc)/ and answer any questions found in the post lab questions for each activity. Prelab Questions
1.
Complete the following table using data for the rye plants’ growth observed at week 8 in Table 1 on the investigative manual. Height at Week 8 (cm)
Difference from Average
Difference squared
Rye plant 1
5.0
-0.33
0.10
Rye plant 2
6.0
0.67
0.44
Rye plant 3
5.0
-0.33
0.10
Average
5.33
Variance
0.22
Standard Deviation
0.47
2.
What does the standard deviation of a data set tell us? Use as an example the meaning of the standard deviation you just calculated in the table in question 1. The standard deviation of a data set is a measure of the dispersion or spread of the data points from the average. It tells us how much individual data points deviate from the mean. In the example of the standard deviation calculated for the heights of Rye Plants 1, 2, and 3, the standard deviation value of approximately 0.4714 means that the heights of these plants are relatively close to the mean height of approximately 5.33 cm.
So, in summary, the standard deviation provides a measure of how consistent or varied
the data points are around the mean, giving insights into the © 2016 Carolina Biological Supply Company
2
dispersion of the data set. This suggests that there isn't much variation in the heights of these particular rye plants at week 8.
3.
Finally, which data had a greater distribution? The wheat plant height at 8-week or the rye plant height at 8-weeks? How do you know? Since the wheat plant had a higher value for standard deviation, it had a greater distribution of growth values at 8 weeks than the rye plant shown above. The percentage by which the plants differed was far lower for the rye plants than for the wheat plants, meaning the growth was more accurately controlled for the rye.
Activity 1
Instructions:
1.
Open the investigative manual. 2.
Read through the entire set of instructions found in the investigative
manual for the activity to avoid making mistakes when you go to execute the experiment. 3.
Once you have read through the instructions go back to step 1 and begin executing the experiment. 4.
Please answer the questions below and/or append appropriate representations of data (photos, graphs, etc).
1.
Insert photos of your hand-drawn graph, completed in step 18 and 19 of Activity 1. The following should be visible/indicated in each photo:
Your name and the date
Data plotted for wheat plant 1, 2, and 3 (for step 18). Data plotted for rye plant (for step 19) 1, 2, and 3.
Axis labels with units
Graph title
Key or legend
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© 2016 Carolina Biological Supply Company
4
Activity 2
Instructions:
1.
Open the investigative manual. 2.
Read through the entire set of instructions found in the investigative
manual for the activity to avoid making mistakes when you go to execute the experiment. 3.
Once you have read through the instructions go back to step 1 and begin executing the experiment. 4.
Please answer the questions below and/or append appropriate representations of data (photos, graphs, etc).
1.
Having now completed a computer-generated graph for the wheat pIants please do the same for the rye plants. Insert your computer-
generated graph of the rye graph plants below. The following should be visible/indicated in each photo:
Data plotted for rye plant 1, 2, and 3.
Axis labels with units
Graph title
Key or legend
0
1
2
3
4
5
6
7
8
9
0
2
4
6
8
10
12
f(x) = 0.99 x
f(x) = 1.06 x + 1.61
f(x) = 1.4 x
Height of Wheat Plant by Week
Wheat Plant 1
Linear (Wheat Plant 1)
Wheat Plant 2
Linear (Wheat Plant 2)
Wheat Plant 3
Linear (Wheat Plant 3)
Time (weeks)
HEIGHT (CM)
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5
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
f(x) = 0.63 x − 0.21
f(x) = 0.68 x + 0.32
f(x) = 0.68 x − 0.68
Height of Rye Plant
Rye Plant 1
Linear (Rye Plant 1)
Rye Plant 2
Linear (Rye Plant 2)
Linear (Rye Plant 2)
Rye Plant 3
Linear (Rye Plant 3)
Linear (Rye Plant 3)
Time (weeks)
Height (cm)
Activity 3
Instructions:
1.
Open the investigative manual. 2.
Read through the entire set of instructions found in the investigative
manual for the activity to avoid making mistakes when you go to execute the experiment. 3.
Once you have read through the instructions go back to step 1 and begin executing the experiment. 4.
Please answer the questions below and/or append appropriate representations of data (photos, graphs, etc).
1.
Shown below is the table you see at the end of activity #3. Please fill it out with the data you generated for the Wheat plant trend lines. Wheat Plant Trendlines
Equations
Wheat Plant 1 trendline equation
Y= 1.2381x + 0.9286
Wheat Plant 1 trendline corrected
Y = 1.402x
Wheat Plant 2 trendline equation
Y = 1.0595x + 1.6071
Wheat Plant 2 trendline corrected
Y= 1.3431x
Wheat Plant 3 trendline equation
Y= 1.0357x – 0.2857
Wheat Plant 3 trendline corrected
Y= 0.9853x
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2.
Based on the corrected trend lines, which wheat plant grew fastest? What was the rate of its growth in cm/week?
Plant 1 grew fastest. The rate of it was 1.402cm/week.
3.
What would be the expected height of plant 2 at 6.5 weeks of growth? What about at 9.5 weeks of growth? Please show your calculation for full credit. Y=1.3431x 6.5= 8.73015cm
Y= 1.3431x 9.5= 12.75945cm
4.
In the above question you were asked to state the height of wheat plant 2 at 9.5 weeks of growth. What has to be assumed to state this expectation? Why? What has to be assumed is the plant will continue to grow at the same speed as the previous eight weeks. This is due to my projection of week 9.5 is based on the average growth per week.
5.
In question 4, above, you were asked what assumption has to be made
to predict the height of wheat plant 2 at 9.5 weeks. Would this be a valid assumption for the plant at week 25, 52, 104? Why or why not? No, this would not be a valid assumption because we need to collect more data to determine the plants potential height at these intervals because 8 weeks is to short of a time frame.
© 2016 Carolina Biological Supply Company