From the Scores at the Right $$\begin{array} { r r } \mathrm { X } & f \\\hline 12 & 2 \\11 & 2 \\10 & 4 \\9 & 7 \\8 & 4 \\6 & 2 \\5 & 1\end{array}$$

Essay

From the scores at the right: $$\begin{array} { r r } \mathrm { X } & f \\\hline 12 & 2 \\11 & 2 \\10 & 4 \\9 & 7 \\8 & 4 \\6 & 2 \\5 & 1\end{array}$$
a. Compute $\sigma$ using the deviation method.
b. Compute $\hat { S }$ using the raw-score method
c. $\hat { S }$ is larger than $\sigma$ . Why must this be so?
d. What is the variance (use $\hat { S }$ )
e. Compute IQR.