Bivariate Data Analysis

Bivariate Data Analysis:

Our bivariate data is the lengths (inches) and weights (grams) of 15 Rainbow trout collected from a Minnesota farm by local university students. We wanted to see if there was any relationship between these variables, and what pattern it followed.

Our Data Values (inches, grams):

(1.8, 0.95), (3.9, 11.11), (4.7, 18.6), (2.2, 1.69), (6.6, 54.43),

(7.2, 71.67), (3.6, 8.85) (5.5, 29.26), (7.8, 90.27), (1.6, 0.68),

(5.9, 37.88), (4.6, 17.69), (2.8, 3.63), (6.1, 43.09), (3.2, 6.26)

Screen Shot 2014-12-15 at 9.14.33 PM

Since the points on the right looked slightly linear, we took 10 more values from older fish and plotted them to see what the relationship was.

Data Values (inches,grams):

(12, 312.98), (9.5, 154.22), (13.3, 431.82),

(10.9, 234.96), (11.4, 267.62), (10.1, 185.97),

(12.6, 361.97), (9.9, 175.99), (13.1, 410.05), (9.4, 149.69)

Screen Shot 2014-12-15 at 9.17.14 PM

Since it leveled out when the fish got older, it shows that they grow very quickly when they are young, but their growth pattern gets more linear when they get older.


The Design

Once my group decided to work with the Rainbow Trout, it was only a matter of time before we formulated our question. Is there a relationship between age, length, and weight, and if so, what is it?

  • observational study
  • sample population (100 fish eggs)
  • population of interest (general population of Rainbow trout from Washington)
  • SRS (simple random sample) of 10 fish every week
  • record age, length, weight
  • count all fish to determine # of deaths

To count the number of fish in the tank, we came up with a few ideas.

  • count by hand
  • take a picture, count off of it
  • pour the fish into several smaller containers, then count

Once we concluded that not one of these three ideas was easy or practical, we sought the help of Mrs. Harrell, who helped us form a mathematical way of counting the dozens of small fish that are clustered in the middle of the tank.

Considering the clustered pattern of the fish, we approximated the volume that the cluster was filling, then approximated how many fish are in a cubic inch of space. Then, we would multiply the number of fish in a cubic inch by the volume that the cluster fills, to get the approximate number of fish left in the tank.