4 A sprinter runs many 100 -metre trials, and the time, \(x\) seconds, for each is recorded. A sample of eight of these times is taken, as follows.
$$\begin{array} { l l l l l l l l }
10.53 & 10.61 & 10.04 & 10.49 & 10.63 & 10.55 & 10.47 & 10.63
\end{array}$$
- Calculate the sample mean, \(\bar { x }\), and sample standard deviation, \(s\), of these times.
- Show that the time of 10.04 seconds may be regarded as an outlier.
- Discuss briefly whether or not the time of 10.04 seconds should be discarded.