# Averaging a matrix

• Sep 26th 2008, 11:51 AM
elomboy
Averaging a matrix
I think I have a good understanding of matrices, but I am having trouble relating it to a word problem. I am given a 5x4 matrix of test scores and asked:

Discuss methods of matrix multiplication that the teacher can use to obtain the information indicated below. In each case, state the matrices to be used and then perform the necessary operations.

a) The average on all four tests for each student, assuming that all four tests are given equal weight.

b) The average on all four tests for each student, assuming that the first three tests are given equal weight and the fourth is given twice this weight

c) The class average on each of the four tests.

• Sep 27th 2008, 12:29 AM
CaptainBlack
Quote:

Originally Posted by elomboy
I think I have a good understanding of matrices, but I am having trouble relating it to a word problem. I am given a 5x4 matrix of test scores and asked:

Discuss methods of matrix multiplication that the teacher can use to obtain the information indicated below. In each case, state the matrices to be used and then perform the necessary operations.

a) The average on all four tests for each student, assuming that all four tests are given equal weight.

b) The average on all four tests for each student, assuming that the first three tests are given equal weight and the fourth is given twice this weight

c) The class average on each of the four tests.

To find a weighted average of the tests on the four tests for each student, where the individual scores on each test comprise the rows of a score matrix $\bold{A}$ , one row for each student you need to compute:

$\bold{Aw}$

where $\bold{w}$ is a column vector of the weights to be applied to each test.

Now for (a) the weights are all $1/4$, for (b) the weights are $1/5,\ 1/5,\ 1/5,\ 2/5$.

To get the class average for each test use the transpose of $\bold{A}$ and weight vector $[1/5,\ 1/5,\ 1/5,\ 1/5,\ 1/5]'$

Try this out and see what you get

RonL
• Oct 13th 2008, 11:25 AM
elomboy
Thank you!
That worked great! I was kicking myself after your post because I didn't see it before.