Mathematics 9709/61 — May/June 2018

In a statistics lesson 12 people were asked to think of a number, $x$, between 1 and 20 inclusive. From the results Tom found that $\sum x = 186$ and that the standard deviation of $x$ is 4.5. Assuming that Tom’s calculations are correct, find the values of $\sum (x - 10)$ and $\sum (x - 10)^2$.