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Zorluk: OrtaMulti-Statement Boolean Evaluation

The table below presents operating and compliance metrics for seven municipal water treatment plants during 2025:

Plant NameDaily Capacity (MGD)Operating Cost ($/MG)Compliance Rate (%)Energy Consumption (kWh/MG)Staff Count
Clearwater Station4532098.4%1,45028
Blue River Plant8028099.1%1,20042
Oak Valley Works3041097.8%1,68022
Pine Creek Facility11025099.5%1,15050
Cedar Ridge Station6034098.9%1,38035
Ironwood Treatment2545096.5%1,75018
Laurel Heights7031098.7%1,30031

Match each statement on the left with its correct boolean evaluation outcome and quantitative justification on the right.

  • Statement I: The plant with the median Staff Count has an Operating Cost greater than the mean Operating Cost of all seven plants.Evaluates to FALSE because the median staff plant (Laurel Heights) has an Operating Cost of 310perMG,whichisbelowtheoverallmeanofapproximately310 per MG, which is below the overall mean of approximately 337.14 per MG.
  • Statement II: For plants with a Compliance Rate above 98.5%, the ratio of total Daily Capacity to total Staff Count exceeds 2.0 MGD per staff member.Evaluates to TRUE because the total capacity of the four qualifying plants (320 MGD) divided by their total staff (158) yields approximately 2.03 MGD per staff member.
  • Statement III: When sorted in ascending order by Energy Consumption, the plant with the third-lowest energy usage has a higher Daily Capacity than the plant with the lowest Operating Cost.Evaluates to FALSE because the plant with the third-lowest energy consumption (Laurel Heights) has a capacity of 70 MGD, which is less than the 110 MGD capacity of the plant with the lowest operating cost (Pine Creek Facility).

Cevap

Statement I matches with the outcome stating it evaluates to FALSE (310<310 < 337.14); Statement II matches with the outcome stating it evaluates to TRUE (2.03 > 2.0); Statement III matches with the outcome stating it evaluates to FALSE (70 MGD < 110 MGD).
Each statement matches its exact evaluation outcome based on standard tabular data calculations: Statement I evaluates to False because 310perMGisbelowthe310 per MG is below the 337.14 per MG mean; Statement II evaluates to True because 320 divided by 158 equals approximately 2.03, which is greater than 2.0; Statement III evaluates to False because a capacity of 70 MGD is less than 110 MGD.

Adım Adım Çözüm

1
Evaluate Statement I by determining the median staff count and mean operating cost.
Sorted staff counts: 18, 22, 28, 31 (Laurel Heights), 35, 42, 50. Median plant is Laurel Heights with an operating cost of 310.Meanoperatingcost=(320+280+410+250+340+450+310)/7=2360/7310. Mean operating cost = (320 + 280 + 410 + 250 + 340 + 450 + 310) / 7 = 2360 / 7 ≈ 337.14. Since 310islessthan310 is less than 337.14, Statement I is False.
Identify the median position (4th out of 7) and compare its specific column value to the unweighted mean across all rows.
2
Evaluate Statement II by filtering plants with compliance > 98.5% and calculating aggregate capacity to staff ratio.
Qualifying plants are Blue River, Pine Creek, Cedar Ridge, and Laurel Heights. Total capacity = 80 + 110 + 60 + 70 = 320 MGD. Total staff = 42 + 50 + 35 + 31 = 158. Ratio = 320 / 158 ≈ 2.025 MGD/staff. Since 2.025 > 2.0, Statement II is True.
Filter rows according to a conditional threshold, aggregate columns across the selected subset, and perform ratio division.
3
Evaluate Statement III by sorting by Energy Consumption and comparing capacities of the 3rd-lowest energy plant and 1st-lowest cost plant.
Energy ordered plants: Pine Creek (1,150), Blue River (1,200), Laurel Heights (1,300). 3rd-lowest is Laurel Heights (Capacity = 70 MGD). Lowest operating cost plant is Pine Creek ($250, Capacity = 110 MGD). Comparing capacities: 70 MGD < 110 MGD. Statement III is False.
Sort table columns independently to locate specified ordinal positions (3rd-lowest energy, 1st-lowest cost) and compare their respective cross-column properties.

Anahtar Kavram

Multi-Statement Boolean Evaluation using tabular sorting, descriptive statistics, conditional filtering, and cross-column ratios.
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