The data provided below consist of measurements \( y_1, y_2, y_3, \) and \( y_4 \) of the ramus bone at four different ages on each of 20 boys.

1. For the dataset:
- (a) Find \( \bar{y} \), \( S \), and \( R \).
- (b) Find \( |S| \) and \( \text{tr}(S) \).

2. For the same dataset in question 1:
- (a) Find \( z \), \( w \), and the variances of \( z \) and \( w \).
- (b) Find \( \text{Cov}(z, w) \).

Data:

\[
\begin{align*}
y_1 & \quad y_2 \quad y_3 \quad y_4 \\
47.8 & \quad 48.8 \quad 49.0 \quad 49.7 \\
46.4 & \quad 47.3 \quad 47.7 \quad 48.4 \\
46.3 & \quad 46.8 \quad 47.8 \quad 48.5 \\
45.1 & \quad 45.3 \quad 46.1 \quad 47.2 \\
47.6 & \quad 48.5 \quad 48.9 \quad 49.3 \\
52.5 & \quad 53.2 \quad 53.3 \quad 53.7 \\
51.2 & \quad 53.0 \quad 54.3 \quad 54.4 \\
49.8 & \quad 50.0 \quad 50.3 \quad 52.7 \\
48.1 & \quad 50.8 \quad 52.3 \quad 54.4 \\
45.0 & \quad 47.0 \quad 47.3 \quad 48.3 \\
51.2 & \quad 51.4 \quad 51.6 \quad 51.9 \\
48.5 & \quad 49.2 \quad 53.0 \quad 55.5 \\
52.1 & \quad 52.8 \quad 53.7 \quad 55.0 \\
48.2 & \quad 48.9 \quad 49.3 \quad 49.8 \\
49.6 & \quad 50.4 \quad 51.2 \quad 51.8 \\
50.7 & \quad 51.7 \quad 52.7 \quad 53.3 \\
47.2 & \quad 47.7 \quad 48.4 \quad 49.5 \\
53.3 & \quad 54.6 \quad 55.1 \quad 55.3 \\
46.2 & \quad 47.5 \quad 48.1 \quad 48.4 \\
46.3 & \quad 47.6 \quad 51.3 \quad 51.8 \\
\end{align*}
\]