Question

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 fishs length affect the mean?
a. the new mean length will be less than 14.2 inches.
b. the new mean length will be 41 inches.
c. the new mean length will still be 14.2 inches.
d. the new mean length will be greater than 14.2 inches.

Explanation:

Step1: Recall mean concept

The mean is the sum of all values divided by the number of values.

Step2: Analyze new value

The original mean is 14.2 inches and a new fish of length 41 inches (which is greater than 14.2 inches) is added.

Step3: Consider impact on mean

When a value greater than the original mean is added to the data - set, the sum of all values increases and the number of values increases by 1. But the increase in the sum is large enough to raise the new mean.

Answer:

D. The new mean length will be greater than 14.2 inches.