High School Mathematics Problems from Alaska

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Investigation of Herring Statistics

Bobbi Jordan

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.

1. In what year was the quota the highest? What was that quota?

1. What year (other than 1977 and 1978) had the lowest quota? What was it?

1. What is the range for the harvest in tons?

1. What percent of the quota was harvested in 1989?

1. In which year was the percent of harvest at its lowest?

1. Find the mean for the ROE Percentage between the years of 1975 and 1996.

1. What year had the longest amount of total time fished? Why did this occur?

1. Which year had the earliest fishing dates? How could the fishermen use the information in the chart about fishing dates?

1. Make a histogram showing the dates of fishing.

1. What do the footnote numbers indicate?

1. In 1996, the fishery was worth 13.86 million dollars. Write this number in standard form.

1. Using your answer in #11, if each of the 52 boats caught the same amount of herring, how much money would each boat make?

1. Under what conditions might the dominant age of the herring be important?

1. In what year, between 1990 and 1996 was the most money made per minute? How much money was made each minute of fishing?

1. 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

1. 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.

1. What is the median of the data?

1. What are the extremes?

1. What are the upper and lower quantities?

1. Are there any outliners?

1. How do you find them?

1. Write a general description about the herring value from the graph that you made. Write in complete sentences.

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