High School Mathematics Problems from Alaska
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Sheet
for the Units and Self-Assessment
for Cultural Standards in Practice.
Investigation
of Herring Statistics
Bobbi
Jordan
bew2@ptialaska.net
MS Word
Download
Standards:
Estimation
and Computation, Statistics and Probability.
Performance
Standards: A3.3.4,
A6.2.3, A.6.3.1, A6.3.2
Concepts: Reading a
fairly complex chart, finding measures of central tendency, making
calculation with large numbers, creating histograms and box
plots.
Carnegie
Chapter: Analyzing
Data and Making Predictions
Overview:
Students
answer a variety of questions using the "Fisherman’s Copy" of
statistics from the Alaska Department of Fish & Game that gives
the history of the Sitka Sac Roe Herring Fishery. This fishery is a
limited entry fishery that occurs every spring in Sitka. The
fishermen are given this data, updated each year, to help them work
with Fish & Game to decide when to open the fishery. For more
information or an updated "Fisherman’s Copy," please contact the
Alaska Department of Fish and Game.
Sitka
Sound Sac Roe Fishery Effort and Value, 1975-1996
|
Year
|
Quota
(tons)
|
Harvest
(tons)
|
Percent
of Quota Harvested
|
Roe
Percent
|
Price/Ton
|
Fishery
Value (millions)
|
Number
of Vessels
|
Number
of Tenders
|
2 hr
Notice In Effect
|
Fishing
Dates
|
Total
Hours Fished (hr:min)
|
Dominant
Age
|
Percent
at Age
|
Foot-note
|
|
1975
|
550
|
1,532
|
279
|
|
|
|
40
|
16
|
|
|
1:30
|
|
|
1
|
|
1976
|
780
|
800
|
103
|
9-11.5
|
|
0.23
|
38
|
26
|
|
4/16
|
4:00
|
|
|
|
|
1977
|
0
|
0
|
0
|
|
|
|
|
|
|
|
|
|
|
|
|
1978
|
|
175
|
70
|
|
|
|
23
|
9
|
|
4/5
|
5:30
|
|
|
|
|
1979
|
2,000
|
2,250
|
113
|
9.34
|
$2,000
|
4.5
|
48
|
50
|
|
4/12
|
NA
|
3
|
65
|
2
|
|
1980
|
4,000
|
4,385
|
110
|
10.8
|
|
|
50
|
76
|
9AM,
4/4
|
4/4,
4/5
|
17:00
|
3
|
11
|
|
|
1981
|
3,000
|
3,506
|
103
|
11.04
|
|
|
51
|
63
|
10PM,
3/23
|
3/24,
3/26
|
4:30
|
5
|
62
|
|
|
1982
|
3,000
|
4,363
|
146
|
11.7
|
|
|
51
|
88
|
2AM,
3/26
|
3/30
|
6:10
|
6
|
57
|
|
|
1983
|
5,500
|
5,450
|
99
|
11.1
|
$760
+ $76/1%
|
4.5
|
51
|
139
|
4AM,
3/23
|
3/26,
3/29
|
10:05
|
3
|
59
|
|
|
1984
|
5,000
|
5,830
|
117
|
11.05
|
$450
+ $45/1%
|
2.8
|
50
|
76
|
10PM,
3/22
|
3/26-3/28
|
11:10
|
4
|
67
|
|
|
1985
|
7,700
|
7,475
|
97
|
11.33
|
$800
+ $80/1%
|
6.77
|
52
|
152
|
6AM,
3/24
|
3/29,
4/1, 4/5
|
6:55
|
5
|
44
|
|
|
1986
|
5,029
|
5,543
|
108
|
11.89
|
$1000
+ $100/1%
|
6.5
|
52
|
99
|
7AM,
3/28
|
4/2,
4/8
|
3:10
|
3
|
36
|
|
|
1987
|
3,600
|
4,216
|
117
|
9.88
|
$1000
+ $100/1%
|
4.17
|
52
|
74
|
7AM,
3/23
|
3/31
|
4:10
|
3
|
53
|
|
|
1988
|
9,200
|
9,575
|
104
|
9.45
|
$500
+ $50/1%
|
4.5
|
52
|
81
|
7AM,
3/25
|
4/4-4/14
|
114:00:00
|
4
|
78
|
2
|
|
1989
|
11,700
|
12,135
|
104
|
9.36
|
$100
+ $10/1%
|
1.21
|
51
|
99
|
6AM,
3/22
|
3/31-4/8
|
88:00:00
|
5
|
77
|
2
|
|
1990
|
4,150
|
3,804
|
92
|
10.6
|
$520
|
1.97
|
52
|
76
|
6AM,
4/4
|
4/5-4/6
|
3:30
|
6
|
71
|
|
|
1991
|
3,200
|
1,908
|
60
|
8.88
|
$106
|
0.2
|
22
|
70
|
7AM,
3/29
|
4/10-4/13
|
78:30:00
|
3
|
75
|
2
|
|
1992
|
3,356
|
5,368
|
160
|
9.38
|
$275
|
1.5
|
52
|
67
|
8AM,
3/30
|
4/6
|
1:23
|
4
|
89
|
|
|
1993
|
9,700
|
10,186
|
105
|
10.67
|
$325
|
3.07
|
50
|
76
|
8AM,
3/26
|
3/27-4/3
|
52:20:00
|
5
|
82
|
2
|
|
1994
|
4,432
|
4,758
|
107
|
11.03
|
$650
+ $65/1%
|
3.4
|
51
|
68
|
8AM,
3/28
|
3/29,
3/31
|
6:45
|
6
|
80
|
|
|
1995
|
2,609
|
2,908
|
111
|
11.8
|
$1100
+ $100/1%
|
3.67
|
51
|
50
|
8AM,
3/23
|
3/25,
3/27
|
3:30
|
7
|
62
|
|
|
1996
|
8,144
|
8,144
|
100
|
9.6
|
|
13.86
|
52
|
97
|
8AM,
3/23
|
3/31-4/8
|
159:00:00
|
3
|
47
|
3
|
28 purse seine and 12 gillnet
vessels participated
Coop fishery
[4168 Competitive (10.1%) with
2000 + 200/1%] & [3976 Cooperative (9.2%0 with 1500 +
150/1%)
Sitka Sound Herring Fishery
Information
|
Year
|
Quota
(tons)
|
Harvest
(tons)
|
Roe
Percent
|
2 hr
Notice In Effect
|
Fishing
Dates
|
Total
Hours Fished (hr:min)
|
Date
of First Spawn
|
Nautical
Miles Spawn
|
Estimated
Escapement (tons)
|
Total
Return (tons)
|
Pre-season
Forecast (tons)
|
ASA
Model Return
|
Foot-note
|
|
1956
|
|
|
|
|
|
|
|
100
|
45,500
|
45,500
|
|
|
|
|
1957
|
|
|
|
|
|
|
|
80
|
36,300
|
36,300
|
|
|
|
|
1958
|
|
|
|
|
|
|
|
93
|
42,200
|
42,200
|
|
|
|
|
1959
|
|
|
|
|
|
|
|
46
|
20,950
|
20,950
|
|
|
|
|
1960
|
|
|
|
|
|
|
|
45
|
20,250
|
20,250
|
|
|
|
|
1961
|
|
|
|
|
|
|
|
NA
|
NA
|
NA
|
|
|
|
|
1962
|
|
|
|
|
|
|
|
NA
|
NA
|
NA
|
|
|
|
|
1963
|
|
|
|
|
|
|
|
NA
|
NA
|
NA
|
|
|
|
|
1964
|
|
234
|
|
|
|
|
1-Apr
|
19
|
8,750
|
8,984
|
|
|
|
|
1965
|
|
315
|
|
|
|
|
8-Apr
|
21
|
9,450
|
9,765
|
|
|
|
|
1966
|
|
340
|
|
|
|
|
8-Apr
|
23
|
10,450
|
10,790
|
|
|
|
|
1967
|
|
268
|
|
|
|
|
5-Apr
|
15
|
6,850
|
7,118
|
|
|
|
|
1968
|
|
260
|
|
|
|
|
31-Mar
|
17
|
7,500
|
7,760
|
|
|
|
|
1969
|
|
573
|
|
|
|
|
8-Apr
|
15
|
6,850
|
7,423
|
|
|
|
|
1970
|
|
743
|
5-10
|
|
|
|
12-Apr
|
11
|
5,150
|
5,893
|
|
|
|
|
1971
|
750
|
676
|
8.3
|
|
|
|
6-Apr
|
9
|
5,950
|
6,636
|
|
6,284
|
1
|
|
1972
|
850
|
558
|
|
|
|
|
28-Apr
|
14
|
6,600
|
7,158
|
|
11,940
|
|
|
1973
|
600
|
597
|
8-9
|
|
|
|
11-Apr
|
10
|
9,400
|
9,997
|
|
10,823
|
|
|
1974
|
600
|
681
|
10-13
|
|
|
3:30
|
13-Apr
|
10
|
3,850
|
4,531
|
|
11,999
|
|
|
1975
|
550
|
1,532
|
10-12
|
|
|
1:30
|
18-Apr
|
8
|
4,900
|
6,432
|
6,400
|
10,743
|
|
|
1976
|
780
|
800
|
9-11.5
|
|
4/16
|
4:00
|
15-Apr
|
13
|
2,350
|
3,150
|
7,300
|
10,243
|
|
|
1977
|
0
|
0
|
|
|
|
|
8-Apr
|
11
|
2,950
|
2,950
|
5,650
|
11,329
|
|
|
Year
|
Quota
(tons)
|
Harvest
(tons)
|
Roe
Percent
|
2 hr
Notice In Effect
|
Fishing
Dates
|
Total
Hours Fished (hr:min)
|
Date
of First Spawn
|
Nautical
Miles Spawn
|
Estimated
Escapement (tons)
|
Total
Return (tons)
|
Pre-season
Forecast (tons)
|
ASA
Model Return
|
Foot-note
|
|
1978
|
|
175
|
10-12
|
|
4/5
|
5:30
|
8-Apr
|
13
|
2,700
|
2,875
|
4,500
|
6,740
|
|
|
1979
|
2,000
|
2,250
|
9.34
|
|
4/12
|
NA
|
13-Apr
|
41
|
17,750
|
20,000
|
20,300
|
20,270
|
2
|
|
1980
|
4,000
|
4,385
|
10.8
|
9AM,
4/4
|
4/4,
4/5
|
17:00
|
3-Apr
|
63
|
35,100
|
39,485
|
39,500
|
37,700
|
|
|
1981
|
3,000
|
3,506
|
11.04
|
10PM,
3/23
|
3/24,
3/26
|
4:30
|
22-Mar
|
60
|
30,000
|
33,506
|
27,000
|
38,962
|
|
|
1982
|
3,000
|
4,363
|
11.7
|
2AM,
3/26
|
3/30
|
6:10
|
24-Mar
|
41
|
29,700
|
34,063
|
30,000
|
25,379
|
|
|
1983
|
5,500
|
5,450
|
11.1
|
4AM,
3/23
|
3/26,
3/29
|
10:05
|
21-Mar
|
68
|
23,250
|
28,700
|
32,750
|
35,559
|
|
|
1984
|
5,000
|
5,830
|
11.05
|
10PM,
3/22
|
3/26
- 3/28
|
11:10
|
21-Mar
|
65
|
38,500
|
44,330
|
30,550
|
49,916
|
|
|
1985
|
7,700
|
7,475
|
11.33
|
6AM,
3/24
|
3/29,
4/1, 4/5
|
6:55
|
29-Mar
|
61
|
30,950
|
38,425
|
38,500
|
38,677
|
|
|
1986
|
5,029
|
5,443
|
11.89
|
7AM,
3/28
|
4/2,
4/8
|
3:10
|
27-Mar
|
52
|
24,750
|
30,193
|
30,950
|
29,045
|
|
|
1987
|
3,600
|
4,216
|
9.88
|
7AM,
3/23
|
3/31
|
4:10
|
21-Mar
|
86
|
46,050
|
50,266
|
24,750
|
44,699
|
|
|
1988
|
9,200
|
9,575
|
9.45
|
7AM,
3/25
|
4/4 -
4/14
|
114:00
|
23-Mar
|
104
|
58,650
|
68,225
|
46,050
|
61,070
|
2
|
|
1989
|
11,700
|
12,135
|
9.36
|
6AM,
3/22
|
3/31
- 4/8
|
88:00
|
19-Mar
|
66
|
27,200
|
39,335
|
58,500
|
35,668
|
2
|
|
1990
|
4,150
|
3,804
|
10.6
|
6AM,
4/4
|
4/5 -
4/6
|
3:30
|
31-Mar
|
39
|
22,750
|
26,554
|
27,200
|
26,145
|
|
|
1991
|
3,200
|
1,908
|
8.88
|
7AM,
3/29
|
4/10
- 4/13
|
78:30
|
1-Apr
|
45
|
23,450
|
25,358
|
22,750
|
38,462
|
2
|
|
1992
|
3,356
|
5,368
|
9.38
|
8AM,
3/30
|
4/6
|
1:23
|
28-Mar
|
73
|
48,600
|
53,968
|
23,450
|
70,778
|
|
|
1993
|
9,700
|
10,186
|
10.67
|
8AM,
3/26
|
3/27
- 4/3
|
52:20
|
24-Mar
|
55
|
35,500
|
45,686
|
48,500
|
41,825
|
2
|
|
1994
|
4,432
|
4,758
|
11.03
|
8AM,
3/28
|
3/29,
3/31
|
6:45
|
28-Mar
|
58
|
14,050
|
18,808
|
28,450
|
32,081
|
|
|
1995
|
2,609
|
2,908
|
11.8
|
8AM,
3/23
|
3/25,
3/27
|
3:30
|
21-Mar
|
37
|
40,150
|
43,058
|
19,700
|
35,441
|
|
|
1996
|
8,144
|
8,144
|
9.6
|
8AM,
3/23
|
3/23,
3/31 - 4/8
|
159:00
|
22-Mar
|
46
|
36,372
|
44,516
|
42,265
|
42,263
|
2
|
1. First year using spawn
deposition
2. Coop fishery
Investigation of Herring
Statistics
Using the
information from Sitka Sound Herring Sac Roe Fishery Effort and
Value, 1975-1996, answer the following questions. If any mathematics
is required to find the solution, show all the work that you did to
arrive at your answer.
- In what year was the quota
the highest? What was that quota?
- What year (other than 1977
and 1978) had the lowest quota? What was it?
- What is the range for the
harvest in tons?
- What percent of the quota
was harvested in 1989?
- In which year was the percent
of harvest at its lowest?
- Find the mean for the ROE
Percentage between the years of 1975 and 1996.
- What year had the longest
amount of total time fished? Why did this occur?
- Which year had the earliest
fishing dates? How could the fishermen use the information in the chart about
fishing dates?
- Make a histogram showing
the dates of fishing.
- What do the footnote numbers
indicate?
- In 1996, the fishery was
worth 13.86 million dollars. Write this number in standard form.
- Using your answer in #11,
if each of the 52 boats caught the same amount of herring, how much money
would each boat make?
- Under what conditions might
the dominant age of the herring be important?
- In what year, between 1990
and 1996 was the most money made per minute? How much money was made each
minute of fishing?
- Does there appear to be a
connection between the dominant age of herring, percentage at that age, and
the percent of roe content? Explain.
Extensions
- Create a box plot of the
data showing fishery value in millions of dollars. Begin with 1976. Be
sure to label axes, indicate intervals, and create a title for the graph.
Answer the
following questions.
- What is the median of the
data?
- What are the extremes?
- What are the upper and lower
quantities?
- Are there any outliners?
- How do you find them?
- Write a general description
about the herring value from the graph that you made. Write in complete sentences.
Table of
Contents
For the Teacher's Guides, please email Alaska
Native Knowledge Network
Handbook
for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be
of interest to anyone involved in bringing local knowledge to bear in school
curriculum. Drawing upon the efforts of many people over a period of several
years, Sidney Stephens has managed to distill and synthesize the critical ingredients
for making the teaching of science relevant and meaningful in culturally adaptable
ways." |
