- An art display consists of an arrangement of \(n\) marbles.
When arranged in ascending order of mass, the mass of the first marble is 10 grams. The mass of each subsequent marble is 3 grams more than the mass of the previous one, so that the \(r\) th marble has mass \(( 7 + 3 r )\) grams.
- Show that the mean mass, in grams, of the marbles in the display is given by
$$\frac { 1 } { 2 } ( 3 n + 17 )$$
Given that there are 85 marbles in the display,
- use the standard summation formulae to find the standard deviation of the mass of the marbles in the display, giving your answer, in grams, to one decimal place.