The average of a dataset is defined as the sum of its elements, divided by how many they are:
[tex] Avg(x_1,\ x_2,\ldots,\ x_n) = \dfrac{x_1+x_2+\ldots+x_n}{n} [/tex]
So, if we call [tex] x [/tex] the unknown weight, we have
[tex] A = \dfrac{x+14.9+15.5+12.6+11.1}{5} = \dfrac{x+54.1}{5} [/tex]
We want this average to be 13.6, so we have
[tex] \dfrac{x+54.1}{5} = 13.6 [/tex]
Multiply both sides by 5:
[tex] x+54.1 = 68 [/tex]
Subtract 54.1 from both sides:
[tex] x = 13.9 [/tex]
So, the heaviest fish weights 14.9 pounds
