1.1. Two geologists are measuring the size of rocks found on a beach in front of a cliff. The geologists record the greatest length, in millimetres, of each rock they find at distances of 5 $m$ and 25 $m$ from the base of the cliff. They randomly choose 20 rocks at each distance.  Their results are summarised in the table below.

Using the formulae  $\overset{¯}{x}=\frac{ \Sigma x}{n}$  and  σ = $\sqrt{\frac{\sum{x}^{2}}{n}-{(\frac{\sumx}{n})}^{2}}$, find the mean and standard deviation for the size of rocks at both 5 $m$ and 25 $m$ from the base of the cliff.

1.2. Compare the location (mean) and spread (standard deviation) of the size of rocks at 5 $m$ and 25 $m$ from the base of the cliff.

1.3. In this instance, an outlier is determined to be any data value that lies outside one standard deviation of the mean ($\overset{¯}{x}$±σ).

(i) Find the smallest rock that is not an outlier at 5 $m$ from the base of the cliff.

(ii) Briefly explain why there cannot be any small rock outliers at 25 $m$ from the base of the cliff.