The density function for the data is
f(x,Q) = 1/2Q -Q <= x1, x2, x3…, xn <Q
So the likelihood is L(Q) = (1/2Q)^n
Since we can’t use calculus, we instead need to choose Q that maximises L(Q)
We need to choose the smallest value we can. But we need to satisfy the inequality above -Q <= x1, x2, x3…, xn <Q,
So the smallest Q we can choose is max |xi|