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Difficulty: MediumCalculating with Data

Astrophysicists measured the transit depth (percentage of starlight blocked) for four exoplanets orbiting a host star at two observation wavelengths (0.5 μm0.5\ \mu\text{m} and 1.5 μm1.5\ \mu\text{m}), as recorded in the table below:

ExoplanetTransit Depth at 0.5 μm0.5\ \mu\text{m} (%)Transit Depth at 1.5 μm1.5\ \mu\text{m} (%)
Exoplanet 11.21.8
Exoplanet 22.52.1
Exoplanet 30.81.6
Exoplanet 43.03.6

True or False: The mean transit depth across all four exoplanets measured at 1.5 μm1.5\ \mu\text{m} is 0.4%0.4\% greater than the mean transit depth measured at 0.5 μm0.5\ \mu\text{m}.

Answer: Answer

Answer

The statement is True.
The mean transit depth at 1.5 μm is 2.275%, and the mean transit depth at 0.5 μm is 1.875%. Subtracting 1.875% from 2.275% gives exactly 0.4%, making the true/false statement correct.

Step-by-Step Solution

1
Calculate the mean transit depth at 0.5 μm.
Sum = 1.2 + 2.5 + 0.8 + 3.0 = 7.5%. Mean = 7.5 / 4 = 1.875%.
Determines the baseline average value for the first wavelength column.
2
Calculate the mean transit depth at 1.5 μm.
Sum = 1.8 + 2.1 + 1.6 + 3.6 = 9.1%. Mean = 9.1 / 4 = 2.275%.
Determines the target average value for the second wavelength column.
3
Calculate the difference between the two averages.
2.275% - 1.875% = 0.4%.
Compares the calculated difference against the claimed value of 0.4%.

Key Concept

Calculating and comparing average values from structured tabular data
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Topics

Calculating with Data

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