Scientists studying the yellow perch, a species of fish, believe that the length of a fish is related to its age. This means that the longer the fish, the older it is. Adult yellow perch vary in size, but they are usually between 10 and 25 centimeters. Scientists at the Great Lakes Water Institute caught, measured, and released yellow perch at several locations in Lake Michigan. The following summary is based on a sample of yellow perch from one of these locations.

length of fish in centimetersnumber of fish
0 to less than 55
5 to less than 107
10 to less than 1514
15 to less than 2020
20 to less than 2524
25 to less than 3030

Use the data to make a histogram that shows the lengths of the captured yellow perch. Each bar should contain the lengths shown in each row in the table.

A blank grid. Labeled fish length in centimeters. Horizontal axis 0 to 30 by 5's. Vertical axis 0 to 40 by 5's.

How many fish were measured? How do you know?
Use the histogram to answer the following questions.

How would you describe the shape of the distribution?

Estimate the median length for this sample. Describe how you made this estimate.
Predict whether the mean length of this sample is greater than, less than, or nearly equal to the median length for this sample of fish? Explain your prediction.
Would you use the mean or the median to describe a typical length of the fish being studied? Explain your reasoning.
Based on your work so far:

Would you describe a typical age for the yellow perch in this sample as: “young,” “adult,” or “old”? Explain your reasoning.
Some researchers are concerned about the survival of the yellow perch. Do you think the lengths (or the ages) of the fish in this sample are something to worry about? Explain your reasoning.