# Whale Of A Time Worksheet

National Council of Teachers of Mathematics
May/June
2008
Whale of a Time
Have you ever wondered about the size of
whales or how many whales exist on Earth?
Many species of whales are
becoming
extinct,
so studying the
characteristics
of
~
whales and how many different
types
remain
on the planet are vital activities. The
U.S.
Fish
and Wildlife Service guarantees protection of
animals under the Endangered
Species
Act.
Scientists examine information to
determine when helping an
animal
species
may
be
necessary.
Let's look at how
is
collected and analyzed.
Data, Data, Data
Imagine you are
part
of a team of
oceanographers
study-
ing
whales.
During the last
week,
the team members have
collected the following information
based on observations
around the
world:
Whale Data
[arranged by observation time)
Type
Length (feet)
Weight (tons)
Gray
13.8
27
Blue
25.1
102
14.5
54
Gray
13.5
21
Gray
13.7
28
14.1
51
Blue
25.7
114
Gray
13.7
31
Gray
13.1
29
Blue
14.9
59
14.2
53
Blue
25.6
116
Gray
14.1
32
14.3
55
Gray
14.0
34
13.9
51
14.8
56
Blue
26.1
119
Blue
26.0
116
15.0
60
r>
Gray
13.0
23
Gray
13.4
24
14.1
58
Gray
12.9
14
Gray
13.7
25
Measures of Central Tendency
When analyzing
data,
scientists and mathematicians
often
use the measures of central
tendency
to have a single
number represent a large set of
numbers.
The three mea-
sures of central tendency are
mean,
median,
and
mode.
The mean of a data set is the sum of the elements in the
data set divided by the number of elements in the data
set.
1.
Determine the mean length of observed bowhead
whales.
5.
The median of a data set is determined
by finding the
middle number of an organized data
set.
A data set is
organized when the elements are listed in order from least
to greatest or greatest to
least.
2.
What is the median length of gray whales? Record your
answer in the table in question 5.
3.
In problem
2,
notice that determining
the median is
straightforward
when a data set has an odd number of
elements.
Is this also true when determining the median
Why,
or why
not?
When a data set has an even number
of elements, the
median is determined
by finding the mean of the two
ele-
ments in the
middle.
4.
What is the median length for observed bowhead
whales?
question 5.
The mode of a data set refers to the
element(s)
that
occur(s) most frequently in the data
set.
5.
Complete the chart for the length of each type of
whale.
Type
Mean
Median
Mode
Blue
Gray
Sometimes one measure is more representative
of the
complete data set than
another.
In some data
sets,
rela-
tively small or relatively large elements (called
outliers)
may affect some measures of central tendency
more
than
others.