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Background: (All the values provided are fictitious.)
I work with data that is in matrix form, and I often have to perform various calculations with this data, such as adding, subtracting, multiplying, and finding averages. We often take measurements called "landing." These measurements give me information about the behavior of the electron beam that scans the CRT screen. I use this data in the design process. The data is measured at predetermined points, so the position of the point is just as important as the actual value. For example, one of our samples might look like this:
14 2 -7 10 -2 Let's call this sample A (or matrix A)
7 2 -5 -5 -1
2 0 -9 3 -4
6 0 0 -1 -6
10 0 7 1 1
I often have more than one landing sample, which means I need to calculate the average of all the samples.
Problem:
You are an engineer in the CRT Engineering group. You have 5 different samples in the landing data: A, B, C, D, and E.
You need to find the average of these five samples in such as way as to find the average value for each position in the matrix. You will need to enter the values into a spreadsheet, as shown below for Sample A. The data for samples B, C, D, and E should be similarly entered.
Sample Data A:
a11 a12 a13 a14 a15
a21 a22 a23 a24 a25
a31 a32 a33 a34 a35
a41 a42 a43 a44 a45
a51 a52 a53 a54 a55
The sample data is given below:
14 2 -7 10 -2 Sample A
7 2 -5 -5 -1
2 0 -9 3 -4
6 0 0 -1 -6
10 0 7 1 1
10 4 -9 12 -1 Sample B
8 2 -10 -5 -1
1 1 -8 4 -6
7 2 2 2 -6
9 1 6 2 2
-2 14 -10 -8 -4 Sample C
-8 3 -9 -6 -4
-4 4 -7 3 -3
8 1 1 0 -7
8 2 8 3 3
-7 -3 -11 14 -2 Sample D
8 2 -10 -5 -1
-8 8 7 2 -3
6 4 0 -3 -5
8 7 5 8 9
10 8 7 5 0 Sample E
8 5 0 -4 -2
3 5 -7 5 -6
6 -2 -1 -1 -4
8 0 5 1 1
The solution to this problem is included in the problem file, available
for
downloading.
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