5.1.1 Final grade calculations using inner product

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Generalizations: 03 Vector Modeling

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Calculate Final Grade

Given the information below, show how we can calculate our final grade using 5.1 Inner Product Between Vectors.

\vec{g} = [\begin{matrix} \frac{q}{300} \\ \frac{e_{1}}{100} \\ \frac{e_{2}}{100} \\ \frac{f}{100} \end{matrix}]

where

The weights for each category are as follows:

Solution. Let's first encode the grade category weights in a $4 \times 1$ vector.

\vec{w} = [\begin{matrix} 0.10 \\ 0.25 \\ 0.25 \\ 0.40 \end{matrix}]

The inner product of the grade vector $\vec{g}$ and the weight vector $\vec{w}$ is our final grade percent score $p$ .

\begin{aligned} p & = \vec{g} \cdot \vec{w} = 0.10 (\frac{q}{300}) + 0.25 (\frac{e_{1}}{100}) + 0.25 (\frac{e_{2}}{100}) + 0.40 (\frac{f}{100}) \end{aligned}