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Difficulty: MediumDescriptive Statistics Interpretation

The table below details physical and operational performance metrics for 10 commercial office properties managed by a real estate investment trust:

Property IDBuilding GradeLeasable Area (sq ft)Occupancy Rate (%)Energy Intensity (kWh/sq ft)
P-101Class A120,00092%18.4
P-102Class B85,00088%22.1
P-103Class A210,00095%14.8
P-104Class A165,00084%19.2
P-105Class B95,00091%24.5
P-106Class A140,00096%16.0
P-107Class B110,00079%21.0
P-108Class A180,00090%15.6
P-109Class A250,00089%17.2
P-110Class B75,00094%23.8

What is the median annual energy intensity, in kWh/sq ft, of the properties that have an occupancy rate of at least 90%?

Answer: 17.2 kWh/sq ft

Answer

17.2
Filtering the table for properties with an Occupancy Rate of at least 90% selects 6 properties: P-101 (18.4), P-103 (14.8), P-105 (24.5), P-106 (16.0), P-108 (15.6), and P-110 (23.8). Sorting these 6 values gives [14.8, 15.6, 16.0, 18.4, 23.8, 24.5]. Since the count is even (N=6N=6), the median is the average of the two middle values, 16.0 and 18.4, which equals 17.2.

Step-by-Step Solution

1
Filter the dataset based on the occupancy rate criteria
Properties meeting the condition (Occupancy Rate ≥90%\ge 90\%) are P-101 (92%), P-103 (95%), P-105 (91%), P-106 (96%), P-108 (90%), and P-110 (94%). This yields a subset of 6 properties.
Only properties meeting the threshold of at least 90% occupancy should be included in the statistical calculation.
2
Extract the corresponding Energy Intensity values for the filtered subset
The corresponding Energy Intensity values (in kWh/sq ft) are: 18.4, 14.8, 24.5, 16.0, 15.6, and 23.8.
Target descriptive metric calculation requires the specific Energy Intensity values for the 6 selected properties.
3
Order the extracted values from smallest to largest
Ordered values: 14.8, 15.6, 16.0, 18.4, 23.8, 24.5.
Finding the median requires arranging numerical data in sequential order.
4
Compute the median for the even-count dataset (N=6N=6)
The 3rd value is 16.0 and the 4th value is 18.4. The median is 16.0+18.42=34.42=17.2\frac{16.0 + 18.4}{2} = \frac{34.4}{2} = 17.2.
When a dataset contains an even number of elements, the median is the arithmetic mean of the two middle elements.

Key Concept

Descriptive Statistics Interpretation
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Topics

Descriptive Statistics Interpretation

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