Ruth from Manchester High School for Girls sent us her work on this problem. Well done, Ruth!

x + y = 2

σ

σ

σ

\sqrt{2}

n

n

n - 1

n

n

n

n - 1

σ

σ

n^{2}

n^{2}

n

σ = \sqrt{n - 1}

In fact, as is explained in the notes , we'd have to do some geometry for (c) to prove that the points are indeed the furthest from the mean. But for this question all we are asked to do is to show that thestandard deviation can take a certain value, and Ruth has done this.