Answer
a) $4.7$
b)
Variance, probability:
0, 3/9
0.5, 2/9
8, 2/9
12.5, 2/9
c) $4.7$
d) Yes
Work Step by Step
a) We know that the average is: $6$. Hence:
$σ^2=\frac{Σ(x−\overline{x})^2}{n}=4.7$
b. We know that:
$s^2=\frac{n[Σ(f)⋅x^2]−[Σ(f⋅x)^2]}{n(n−1)}$
Hence we can obtain:
Variance, probability:
0, 3/9
0.5, 2/9
8, 2/9
12.5, 2/9
c) Using the equation for the mean, we can see that the mean of the above table is $4.7$.
d Yes, it is. Finally, we can see that it has the same value as $σ^2$, hence it is an unbiased predictor.
