Whale Of A Time Worksheet Page 4
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1
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4Whale of a
Time-continued
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Editor:
Ed Nolan, Albert Einstein High
School,
Kensington, MD 20895
EditorialPanel:
Melissa Boston, Duquesne University,Pittsburgh, PA 15282
Juli K. Dixon, Universityof Central
Florida,Orlando,
FL 32816
Mark Evans, Garden Grove, CA 92843
Linda Ferreira,Attleboro Public
Schools,
Attleboro, MA 02703
Terri Moore, Parkway Southwest Middle School, Ballwin, MO 63021
Marshalyn Baker, MessalonskeeMiddle
School, Oakland,
ME 04963
Sandy Berger
Luanne Flom
Rebecca Totten
Answers
1. The mean length of bowhead whales is about 14.36
feet.
2. The median length of gray whales is 13.7
feet.
3.
No,
because eight elements are in the data set; no single
element is in the middle.
4. The median length for bowhead whales is 14.25
feet.
5.
Type
Mean
Median
Mode
Blue
23.9 feet
25.65 feet
None
Bowhead
-14.36 feet
14.25 feet
14.1 feet
Gray
-13.54 feet
13.70 feet
13.7 feet
6. The measure of central tendency that best represents blue
whales'
length is the median. It is less influenced
by the rela-
tively small length of 14.9 and is most like the majority of the
data. The measure that best represents the bowhead whale
could be either the mean or the median because the data
has no outliers. The measure
that
best represents the gray
whale could be the
mean,
the median, or the mode because
all are within the span of most of the data.
7.
Lengths of Bowhead Whales Compared to Gray Whales
Bowhead
Gray
12 9
9
13 01457778
853211
14 01
o
15
Key: 8114
=
14.8 feet
1317
=
13.7 feet
8. It appears that bowhead whales are longer because most of
the data for bowheads
are on the stem representing
14
feet
of
length,
whereas most of the data for grays are on the stem
representing
13 feet of
length.
9. a.
The lower extreme for bowhead whale length is 13.9 feet;
for gray
whales,
12.9
feet.
b.
The upper extreme for bowhead whale
length
is 15 feet;
for gray whales, 14.1
feet.
c. The median for bowhead whale length is 14.25 feet; for
gray
whales,
13.7
feet.
10.
The lower quartile for bowhead whale
length
is 14.1
feet.
11. The lower quartile for gray whale length is
13.1
feet.
12. The upper quartile for bowhead whale length is 14.65 feet;
for gray whales, 13.8
feet.
13.
Whale Length
--{[}--
Bowhead whale
~Graywhale
~ I
I I I I I
I
I
I
I I I
I
I I
I I
I
I
I
I ~
12
13
14
15
16
Board
Liason:
EditorialCoordinator:
Production Editor:
Production
Specialist:
14. No, the box-and-whisker
plot shows that each of the num-
bers in the five-number
summary is greater for bowhead
whales than it is for gray whales. In
fact,
75 percent of the
bowhead whales are longer than any of the gray
whales.
15.
Blue Whale Length versus Weight
140
120
~
It.
fJ)
§
100
~
80
s:
Ol
60
~
40
20
o
o
25
30
5
10
15
20
Length in feet
The relationship
appears to be that when the length of a blue
whale
increases,
the weight also
increases.
16. Sample answer: The line of best fit is approximately
y
=
5.1
x
-
17.63. The meaning of the slope of 5.1 is that
a blue whale increases its weight 5.1 tons for every 1 foot
increase in length.
17. Sample answer: The estimate for the weight of a 22-foot-long
blue
whale,
based on the line of best fit, is 94.57
tons.
18.
The mean of the data set is 23.88
feet;
the median is 24
feet;
and the data has two modes (22 and 24). Either the mean or
the median is representative
of the data set because there
are no significant extreme
values.
19. Answers will vary based on the number of objects removed
from the population.
20. Answers will vary based on the number of Objects removed
from the population the second time.
21. Answers will vary but should be the solution to the proportion
described.
(~l
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COUNCIL
OF
TEACHERS
OF MATHEMATICS
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