Whale Of A Time Worksheet Page 3

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Whale of a
Time-continued
best fit can be added to demonstrate
what relationship
may exist
among the
variables, and,
when added to the
plot.
helps show
the strength of the relationship.
The easiest way to determine the
equation of the line of best fit is using a graphing
calculator.
15. Create a scatter plot of a blue whale's length compared
to its
weight.
Describe any relationship you see between the two
variables.
16. What is the equation of the line of best fit for the scatter plot?
Plot the line on the scatter
plot.
What is the meaning of this
line's slope?
17.
If you estimate a blue whale's length at 22 feet, what would
you estimate its weight to be?
A more detailed survey of gray whales determined
the following
information:
Length in Feet
Frequency
15
1
16
0
17
2
18
5
19
4
20
2
21
1
22
6
23
3
24
6
25
1
26
2
27
3
28
5
29
4
30
1
31
2
32
1
33
0
34
0
35
1
18.
The frequency table shows that of the 50 whales in the
survey,
some of the lengths appeared
more than
once.
Determine the measures of central tendency for these data.
Which do you think best represents the data set? Why?
Capture and
ReCapture*
As stated
above,
it is important to study not only whale char-
acteristics but also their populations'
growth or decline. As you
can imagine, determining
an accurate estimate of the number
of
whales,
which spend a great deal of time
underwater,
is very
difficult! Many whale population
estimates are based on obser-
vations,
which vary widely depending
on observers, time of year,
and weather
conditions.
The National Marine Fisheries Service
has clear rules for observing
and counting whales. Sampling is
one of the important mathematical
techniques
used to determine
the populations of different whale types.
('Here
is an experiment you can do to see how sampling
works.
Collect something small, like navy
beans,
pennies, or tiles (you
do not want to know how many you have). For this activity, we
will refer to each of these pieces as
"whales."
Place all of the
whales in a container large enough to hold them. Reach in and
pick out a
handful.
Count them and then mark them in some way
(with a felt-tip
marker,
by putting tape over them,
etc).
19. How many whales did you remove and mark?
_
Replace the marked whales. Shake the container or otherwise
mix the contents to simulate the natural movement of
whales.
Now, draw out another handful of
whales.
20. How many whales are in your second sample?
_
How many of them are marked?
_
We can use proportional
reasoning to determine how many
whales are in the container. In our sampling, we assume that the
ratio of marked whales in the second handful is the same as the
ratio of the entire
population.
So,
marked whales in handful 2
total whales in handful 2
marked whales in handful 1
total whale population
21.
Using the proportion above, what is your estimate for the
total whale population?
Can You
...
determine the meaning of a 95% confidence
interval? (The
International Whaling Commission
estimates that the number of
gray whales in the Western North Pacific in 2007 was 121 with
a 95% confidence
interval between 112 and 130.)
determine the correlation coefficient of the line of best fit for the
data on the blue whale? (The line of best fit refers to how well
the line actually fits to the data set)
Did You Know That
...
• a blue whale's heart is about the size of a Volkswagen Beetle
car,
and a person could crawl through the aorta (a major blood
vessel) of the blue whale?
a humpback
whale's four-chambered
heart weighs about 430
pounds,
about as much as three average adult humans?
a blue whale is the loudest and largest animal that has ever
lived on the Earth?
a sperm whale has the largest brain of any
animal,
weighing
about 20 pounds?
Mathematical
Content
Measures of central tendency, stern-and-leaf
plots,
box-and-
whisker plots, scatter plots, line of best
fit, sampling,
proportional
reasoning
Resources
Enchanted Learning, "All about
Whales,"
International Whaling Commission,
National Marine Fisheries Service Alaska Region, "Pacific Gray
Whale Population Estimate
Released,"
news
release,
May 10,
2002.
0502.htm.
NCTM Student Math
Notes,
May 2008
*We would like to
acknowledge
and thank Rachel
Curto,
who contributed
the Capture and ReCapture
idea.
3

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