A neuroscientist measures the reaction times (in seconds) during an experimental session in a sample of cocaine-addicted (n = 8), morphine-addicted (n = 6), and heroin-addicted rats (n = 12). Mean reaction times in each sample were 12, 13, and 17 seconds, respectively. What is the weighted mean for all three samples? Hint: The overall mean is not 14.0 seconds. (Round your answer to two decimal places.)

14.54

Step-by-step explanation:

In a weighted average a "weight" is associated to each value.

The weighted mean is computed the following way:

Suppose you want to calculate the weighted mean of the values

a1, a1, ..., an

with weights

w1, w2, ..., wn

Then

Weighted mean = (w1*a1+w2*a2 + ... + wn*an) / (w1+w2 + ... + wn)

In this case we have

a1 = 12, w1 = 8

a2 = 13, w2 = 6

a3 = 17, w3 = 12

Weighted mean

(12*8+13*6+17*12) / (8+6+12) = 14.54 rounded to 2 decimal places.