The mean length of a group of fish is 14.2 inches. A fish that is 41 inches long joins the group. How does this fish’s length affect the mean?

The mean length of a group of fish is calculated by adding up all the lengths of the fish in the group and then dividing by the number of fish.

Step 1: Let's assume the group has 'n' number of fish. So, the total length of all the fish in the group before the 41-inch fish joined is 14.2n (mean length * number of fish).

Step 2: When the 41-inch fish joins the group, the total number of fish becomes n+1 and the total length becomes 14.2n + 41.

Step 3: The new mean length is calculated by dividing the total length by the total number of fish, which is (14.2n + 41) / (n + 1).

Since 41 inches is significantly larger than the original mean of 14.2 inches, it will increase the mean length of the group of fish. The exact amount of increase will depend on the original number of fish in the group (n). The larger the original group, the smaller the impact of one 41-inch fish on the mean length.