Overview
Out of Balance
Part I Individual Assignment
In this experiment you are attempting to find the most reliable way to estimate the mass of a strawberry without the use of a scale, by first finding a correlation between the height, width and depth (chose your width to be larger than the depth) of a strawberry and its mass. You will take linear measurements of three dimensions of the strawberries in a 1-lb sample and plot them Vs. the mass of the strawberry to determine which if any of the three measurements best correlates to the mass.
In this experiment you will record the measurements of each strawberry in a table similar to the following.
Strawberry Mass (g) Height (cm) Width (cm) Depth (cm) MEF
1
2
3
4
The better the correlation between the dimension of the fruit and its mass, the closer the data points will be to forming a straight line. You can judge which dimension most closely correlates with the mass by comparing the plots of each individual dimension Vs. the mass. Excel offers a convenient tool to evaluate your data. For tips on how to use excel watch the video in Canvas.
Here is a data sample collected from a 1-lb container of strawberries harvested during a non-ideal harvest season (they were all rather small).
Strawberry M (g) H (cm) W (cm) D (cm)
1 23 4.2 3.4 3.6
2 19 3.85 3.52 2.48
3 17 3.35 3.5 3.16
4 18 4 3.22 3
5 16 3.86 3.12 2.78
6 22 3.72 4.12 2.9
7 18 3.8 3.78 3.22
8 23 4 3.48 3.12
9 18 3.75 3.62 2.63
10 15 4.5 3.72 3.11
11 17 4.36 3 2.55
12 12 3.46 2.8 2.45
13 21 3.62 3.51 3.08
14 14 4.92 2.81 2.59
15 15 3.35 3.28 2.9
16 13 3.12 3.5 2.21
17 18 4.08 3.5 2.95
18 11 3.55 2.55 2.39
19 16 3.7 3.19 3
20 10 3.32 2.7 2.55
21 9 3.41 3.69 2.41
22 12 3.88 2.9 2.8
23 12 3.81 2.8 2.75
24 11 3.54 2.94 2.54
25 13 4.1 2.95 2.55
26 10 3.5 2.7 2.5
It is difficult to assess how well the mass corresponds to each of the linear measurements when they are in table form, but it is significantly easier when the data is plotted.
We can see that for this particular data set, the depth has the best correlation (The R2 value is closer to 1). However, none of them correlate particularly well.
You will combine the dimensions using simple arithmetic operations to improve the correlation between a number derived from the linear measurements and the mass (for example Height x width x depth, or Height + width + depth, or Height x width/depth, etc.). Whichever combination gives you the most nearly linear plot will be your proposed “mass estimation formula”. You will apply the formula to your data set and show that it works better than the individual measurements. Here is the graph derived from the formula I used (which is secret).
The R2 value for this plot shows a 31% improvement over the best linear measurement, and it can be improved further by tinkering with the formula. Your goal is to come up with the mathematical formula that gives you the best correlation.
Your Lab report should include your data, your labeled graphs (4 of them) and the mass estimation formula you invented. Be sure to follow the lab report format posted in Canvas.