3 The marks \(x\) scored by a sample of 56 students in an examination are summarised by
$$n = 56 , \quad \Sigma x = 3026 , \quad \Sigma x ^ { 2 } = 178890 .$$
- Calculate the mean and standard deviation of the marks.
- The highest mark scored by any of the 56 students in the examination was 93 . Show that this result may be considered to be an outlier.
- The formula \(y = 1.2 x - 10\) is used to scale the marks. Find the mean and standard deviation of the scaled marks.