Let z1,...,zn ∈ R and set ¯z = (1/n) n i=1 zi. (a) Show, for any c ∈ R, 1 n n i=1 |c − zi| 2 = |c − z¯| 2 + 1 n n i=1 |z¯ − zi| 2 . (b) Conclude from (a): 1 n n i=1 |z¯ − zi| 2 = min c∈R 1 n n i=1 |c...

Let z1,...,zn ∈ R and set ¯z = (1/n) n i=1 zi.

(a) Show, for any c ∈ R, 1 n n i=1 |c − zi| 2 = |c − z¯| 2 + 1 n n i=1 |z¯ − zi| 2 .

(b) Conclude from (a): 1 n n i=1 |z¯ − zi| 2 = min c∈R 1 n n i=1 |c − zi| 2 .