Question

its not an easy life, but its a good life! suppose you decide to take the summer off and sign on as a deck hand for a commercial fishing boat in alaska that specializes in deep - water fishing for groundfish. what kind of fish can you expect to catch? one way to answer this question is to examine the reports on groundfish caught in the gulf of alaska. the following list indicates the types of fish caught annually in thousands of metric tons: flatfish, 36.3; pacific cod, 68.6; sablefish, 16.0; walleye pollock, 71.2; rockfish, 18.9. make a pareto chart showing the annual harvest for commercial fishing in the gulf of alaska.

Explanation:

Step1: Order the data by frequency (descending)

First, we sort the fish types by their annual harvest (in thousands of metric tons) in descending order:

• Walleye Pollock: 71.2
• Pacific cod: 68.6
• flatfish: 36.3
• rockfish: 18.9
• sablefish: 16.0

Step2: Calculate cumulative frequency and cumulative percentage

First, find the total harvest: \( 71.2 + 68.6 + 36.3 + 18.9 + 16.0 = 211 \) (thousands of metric tons).

Then, calculate cumulative frequency and cumulative percentage for each category:

• Walleye Pollock:
• Cumulative Frequency: \( 71.2 \)
• Cumulative Percentage: \( \frac{71.2}{211} \times 100 \approx 33.74\% \)
• Pacific cod:
• Cumulative Frequency: \( 71.2 + 68.6 = 139.8 \)
• Cumulative Percentage: \( \frac{139.8}{211} \times 100 \approx 66.26\% \)
• flatfish:
• Cumulative Frequency: \( 139.8 + 36.3 = 176.1 \)
• Cumulative Percentage: \( \frac{176.1}{211} \times 100 \approx 83.46\% \)
• rockfish:
• Cumulative Frequency: \( 176.1 + 18.9 = 195 \)
• Cumulative Percentage: \( \frac{195}{211} \times 100 \approx 92.42\% \)
• sablefish:
• Cumulative Frequency: \( 195 + 16.0 = 211 \)
• Cumulative Percentage: \( \frac{211}{211} \times 100 = 100\% \)

Step3: Create the Pareto chart

• Bar Graph (Left Y - axis): For each fish type (on the X - axis), draw a bar with height equal to its annual harvest (in thousands of metric tons).
• Line Graph (Right Y - axis): Plot the cumulative percentage values calculated above, with the X - axis values corresponding to the ordered fish types. The line should connect the cumulative percentage points for each category.

Answer:

To create the Pareto chart:

1. Ordered Data (by harvest, descending):

Fish Type	Harvest (thousands of metric tons)
Pacific cod	68.6
flatfish	36.3
rockfish	18.9
sablefish	16.0

2. Cumulative Data:

Fish Type	Harvest	Cumulative Harvest	Cumulative Percentage (\%)
Pacific cod	68.6	139.8	\( \approx 66.26 \)
flatfish	36.3	176.1	\( \approx 83.46 \)
rockfish	18.9	195.0	\( \approx 92.42 \)
sablefish	16.0	211.0	\( 100.00 \)

3. Pareto Chart Construction:

• Bar Plot: On the X - axis, place the fish types in the ordered (descending harvest) order. On the left Y - axis, use the scale for "Harvest (thousands of metric tons)". Draw a bar for each fish type with height equal to its harvest value.
• Line Plot: On the same X - axis, use the right Y - axis with a scale for "Cumulative Percentage (\%)". Plot the cumulative percentage values from the table above and connect them with a line.

The Pareto chart will visually show the individual harvests (via bars) and the cumulative percentage of the total harvest (via the line), helping to identify the "vital few" fish types that contribute the most to the total groundfish harvest in the Gulf of Alaska.