<Dd> 4 + 36 + 45 + 50 + 75 5 = 210 5 = 42 . (\ displaystyle (\ frac (4 + 36 + 45 + 50 + 75) (5)) = (\ frac (210) (5)) = 42 .) </Dd> <P> The geometric mean is an average that is useful for sets of positive numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean) e.g. rates of growth . </P> <Dl> <Dd> x _̄ = (∏ i = 1 n x i) 1 n = (x 1 x 2 ⋯ x n) 1 / n (\ displaystyle (\ bar (x)) = \ left (\ prod _ (i = 1) ^ (n) (x_ (i)) \ right) ^ (\ tfrac (1) (n)) = \ left (x_ (1) x_ (2) \ cdots x_ (n) \ right) ^ (1 / n)) </Dd> </Dl> <Dd> x _̄ = (∏ i = 1 n x i) 1 n = (x 1 x 2 ⋯ x n) 1 / n (\ displaystyle (\ bar (x)) = \ left (\ prod _ (i = 1) ^ (n) (x_ (i)) \ right) ^ (\ tfrac (1) (n)) = \ left (x_ (1) x_ (2) \ cdots x_ (n) \ right) ^ (1 / n)) </Dd>

Give detailed description of different types of 'mean' used in statistics