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Difficulty: MediumCalculating with Data

Plant physiologists measured the photosynthetic rate (in μmol CO2/m2⋅s\mu\text{mol CO}_2/\text{m}^2\cdot\text{s}) of a C3 plant species exposed to three ambient temperature conditions (20∘C20^\circ\text{C}, 30∘C30^\circ\text{C}, and 40∘C40^\circ\text{C}) under constant saturating light intensity. The measured photosynthetic rates were 15.0 μmol CO2/m2⋅s15.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s} at 20∘C20^\circ\text{C}, 24.0 μmol CO2/m2⋅s24.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s} at 30∘C30^\circ\text{C}, and 9.0 μmol CO2/m2⋅s9.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s} at 40∘C40^\circ\text{C}.

Based on these data, is the following statement True or False?
"The mean photosynthetic rate of the plant across the three tested temperatures is 16.0 μmol CO2/m2⋅s16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}."

Answer: Answer

Answer

True. The mean photosynthetic rate across all three tested temperatures is 16.0 μmol CO2/m2⋅s16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}.
The calculated average of the three photosynthetic rates (15.015.0, 24.024.0, and 9.09.0) is 15.0+24.0+9.03=48.03=16.0 μmol CO2/m2⋅s\frac{15.0 + 24.0 + 9.0}{3} = \frac{48.0}{3} = 16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}, which matches the claim directly.

Step-by-Step Solution

1
Extract the photosynthetic rates for all three temperature conditions.
Rate at 20∘C=15.020^\circ\text{C} = 15.0, Rate at 30∘C=24.030^\circ\text{C} = 24.0, Rate at 40∘C=9.040^\circ\text{C} = 9.0.
Identifying all data points is required to calculate the overall average.
2
Sum the rates recorded across the three conditions.
15.0+24.0+9.0=48.0 μmol CO2/m2⋅s15.0 + 24.0 + 9.0 = 48.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}.
Finding the total sum is the first step in calculating an arithmetic mean.
3
Divide the total sum by the total number of conditions (n=3n = 3).
48.03=16.0 μmol CO2/m2⋅s\frac{48.0}{3} = 16.0\ \mu\text{mol CO}_2/\text{m}^2\cdot\text{s}.
Dividing the sum by the count yields the correct mean value.

Key Concept

Calculating Arithmetic Mean from Data Points
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Topics

Calculating with Data

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