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Zorluk: ZorCalculating with Data

Soil ecologists evaluated nitrogen mineralization by measuring nitrate production rates (in mg/kg/day\text{mg/kg/day}) across 4 depth zones in two distinct forest management plots (Plot X and Plot Y). The results are summarized in Table 1 below.

Depth ZonePlot X Nitrate Rate (mg/kg/day\text{mg/kg/day})Plot Y Nitrate Rate (mg/kg/day\text{mg/kg/day})
0–10 cm5.09.0
10–20 cm3.56.5
20–30 cm2.04.0
30–40 cm1.52.5

Based on Table 1, if a composite sample is created using equal masses of soil from all 4 depth zones (0–40 cm), by how much does the average nitrate production rate of Plot Y exceed the average nitrate production rate of Plot X?

  1. 2.5 mg/kg/day2.5\text{ mg/kg/day}Cevap
  2. B
    4.0 mg/kg/day4.0\text{ mg/kg/day}
  3. C
    5.5 mg/kg/day5.5\text{ mg/kg/day}
  4. D
    10.0 mg/kg/day10.0\text{ mg/kg/day}

Cevap

The average nitrate production rate of Plot Y exceeds that of Plot X by 2.5 mg/kg/day2.5\text{ mg/kg/day}.
The composite average rate for Plot Y is calculated by summing its four depth zone values (9.0+6.5+4.0+2.5=22.09.0 + 6.5 + 4.0 + 2.5 = 22.0) and dividing by 44, yielding 5.5 mg/kg/day5.5\text{ mg/kg/day}. The composite average rate for Plot X is calculated similarly (5.0+3.5+2.0+1.5=12.05.0 + 3.5 + 2.0 + 1.5 = 12.0) and divided by 44, yielding 3.0 mg/kg/day3.0\text{ mg/kg/day}. The difference between these two averages is 5.5−3.0=2.5 mg/kg/day5.5 - 3.0 = 2.5\text{ mg/kg/day}.

Adım Adım Çözüm

1
Calculate the average nitrate production rate for Plot Y across the 4 depth zones.
Average for Plot Y = 9.0+6.5+4.0+2.54=22.04=5.5 mg/kg/day\frac{9.0 + 6.5 + 4.0 + 2.5}{4} = \frac{22.0}{4} = 5.5\text{ mg/kg/day}.
An equal-mass composite sample over 0–40 cm requires finding the arithmetic mean of all 4 depth intervals.
2
Calculate the average nitrate production rate for Plot X across the 4 depth zones.
Average for Plot X = 5.0+3.5+2.0+1.54=12.04=3.0 mg/kg/day\frac{5.0 + 3.5 + 2.0 + 1.5}{4} = \frac{12.0}{4} = 3.0\text{ mg/kg/day}.
The same averaging procedure must be applied to Plot X to determine its overall composite rate.
3
Subtract the average rate of Plot X from the average rate of Plot Y.
5.5 mg/kg/day−3.0 mg/kg/day=2.5 mg/kg/day5.5\text{ mg/kg/day} - 3.0\text{ mg/kg/day} = 2.5\text{ mg/kg/day}.
The question asks by how much Plot Y's composite average exceeds Plot X's composite average.

Anahtar Kavram

Calculating mean values from multi-source tabular data and determining net differences between treatments.
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Konular

Calculating with Data

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