library(ggplot2)
Grades <- c(49, 61, 62, 64, 64, 67, 72, 73, 75, 75, 80, 82, 86, 88, 89)
summary(Grades)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 49.0 64.0 73.0 72.5 81.0 89.0
c <- qplot(Grades, main = "Midterm 2 Grade Distribution", binwidth = 5)
c + geom_histogram(fill = "darkgray", color = "black", binwidth = 5)
| Problem | Concept | Class Average |
|---|---|---|
| 1 | Nullspace and column space | 78.00% |
| 2 | Finding determinants | 87.78% |
| 3 | Abstract eigenvalues | 40.00% |
| 4 | Characteristic polynomials | 68.33% |
| 5 | Linear transformations and area | 69.17% |
| 6 | Definitions | 78.33% |
| 7 | Eigenvalues and invertibility | 68.33% |
| 8 | 2-by-2 inverse formula | 61.11% |
| 9 | Eigenspaces and diagonalization | 71.67% |
| 10 | Eigenvectors and eigenvalues | 78.33% |
| 11 | Matrix inverse algorithm | 95.00% |
| 12 | Properties of determinants | 10.00% |