Descriptive Statistics Interpretation Practice Questions — GMAT

The table below displays the financial metrics for six companies operating across two industry sectors:

Company	Sector	Revenue ($M)	R&D Spend ($M)
Alpha Therapeutics	Biotech	120	30
Beta Bio	Biotech	200	50
Gamma Tech	IT	450	40
Delta Pharma	Biotech	160	40
Epsilon Health	Biotech	320	70
Zeta Systems	IT	500	60

Statement: For the subset of companies operating in the Biotech sector, the median annual revenue is $180 million.

True

False

Show answer & explanation

Answer: True

Answer

True

Filtering for Biotech companies gives revenues of

120M,

160M,

200M, and

320M. With 4 items, the median is the average of the 2nd and 3rd terms:

(160 + 200) / 2 = 180

million dollars.

Step-by-Step Solution

1

Filter the dataset by Sector

Identified the four Biotech companies: Alpha Therapeutics (

120M), Beta Bio (

200M), Delta Pharma (

160M), and Epsilon Health (

320M).

The statement specifically concerns companies in the Biotech sector.

2

Sort the filtered revenues in ascending order

Ordered revenues:

120M,

160M,

200M,

320M.

Determining the median requires data elements to be ordered sequentially.

3

Calculate the median for an even-count dataset

Middle two values are

160M and

200M. Median = (

160M +

200M) / 2 = $180M.

For an even number of observations

N = 4

, the median is the arithmetic mean of the

(N/2)^{\text{th}}

and

(N/2 + 1)^{\text{th}}

elements.

Key Concept

Calculating the median of a filtered table subset with an even number of items

Estimated Time:45s

Question 2Question →

The table below displays the industry sector, annual revenue (in millions of dollars), and number of employees for 10 tech startups.

Startup Name	Industry Sector	Annual Revenue ($M)	Employees
Apex Systems	Software	14	45
Beacon Health	Healthcare	30	110
Crest Tech	Software	42	160
Dome Logistics	Logistics	20	80
Echo Labs	Software	35	140
Flux Interactive	Software	52	210
Grid Solutions	Energy	65	190
Horizon Soft	Software	24	95
Impulse Media	Software	18	65
Jade Bio	Healthcare	32	125

Based on the table, what is the median annual revenue, in millions of dollars, for the startups in the Software sector?

24.0

29.5

31.0

35.0

43.5

Show answer & explanation

Answer: 29.5

Answer

29.5

Filtering the dataset for startups in the Software sector yields 6 revenue figures:

14M,

18M,

24M,

35M,

42M, and

52M. Sorting these values in ascending order gives: 14, 18, 24, 35, 42, 52. Since

N = 6

is an even number, the median is the arithmetic mean of the 3rd and 4th values:

\frac{24 + 35}{2} = 29.5

.

Step-by-Step Solution

1

Filter the table for startups in the Software sector.

Identified 6 Software startups with revenues of

14M,

42M,

35M,

52M,

24M, and

18M.

The question specifies restricting calculations to startups in the Software sector.

2

Sort the filtered revenues in ascending numerical order.

Sorted list: 14, 18, 24, 35, 42, 52.

Determining the median requires ordering data from smallest to largest.

3

Calculate the median for the even dataset (

N = 6

).

The two central numbers are the 3rd value (24) and the 4th value (35). The median is

\frac{24 + 35}{2} = 29.5

.

When

N

is even, the median is the average of the two middle elements.

Key Concept

Descriptive Statistics Interpretation

Estimated Time:1m 30s

Question 3Question →

The table below provides operational data for eight solar power facilities across two regions:

Facility Name	Region	Capacity (MW)	Operational Efficiency (%)
Solaria Alpha	North	120	88
Solaria Beta	South	150	91
Solaria Gamma	North	200	97
Solaria Delta	North	110	82
Solaria Epsilon	South	180	89
Solaria Zeta	North	135	92
Solaria Eta	North	160	94
Solaria Theta	North	140	85

What is the median operational efficiency, in percent, of the solar power facilities located in the North region?

Show answer & explanation

Answer: 90

Answer

The median operational efficiency of the solar power facilities in the North region is 90%.

Filtering the table for facilities in the North region yields six efficiency values: 82%, 85%, 88%, 92%, 94%, and 97%. Because the dataset contains an even count of six values, the median is the average of the two middle values (88% and 92%). Calculating

\frac{88 + 92}{2}

gives 90%.

Step-by-Step Solution

1

Filter the table to isolate facilities in the North region.

Identified 6 facilities with operational efficiency values: 88%, 97%, 82%, 92%, 94%, and 85%.

The stem specifies evaluating descriptive statistics for the North region subset only.

2

Sort the efficiency values of the filtered subset in ascending order.

Ordered set: {82, 85, 88, 92, 94, 97}.

Calculating the median requires ordering data points from lowest to highest.

3

Compute the arithmetic mean of the two central terms in the 6-element dataset.

\frac{88 + 92}{2} = 90

.

For an even-count set of

N = 6

items, the median is defined as the average of the

\frac{N}{2}

-th (3rd) and

(\frac{N}{2} + 1)

-th (4th) terms.

Key Concept

Descriptive Statistics Interpretation (Median of Even-Count Subsets)

Question 4Question →

The table below displays operational performance metrics for 10 regional cold-chain distribution centers operated by a pharmaceutical logistics company across two geographic zones.

Distribution Center	Zone	Cold Storage Volume ( $10^3\text{ m}^3$ )	Temperature Excursions	On-Time Delivery Rate (%)
Center H-1	Zone East	45	12	94.2
Center H-2	Zone West	80	18	91.5
Center H-3	Zone East	60	8	96.8
Center H-4	Zone East	30	22	89.0
Center H-5	Zone West	55	14	93.4
Center H-6	Zone East	75	5	98.1
Center H-7	Zone West	40	16	92.0
Center H-8	Zone East	90	11	95.5
Center H-9	Zone West	65	9	95.0
Center H-10	Zone East	50	15	92.6

By how many percentage points does the median On-Time Delivery Rate of the distribution centers in Zone East exceed the mean On-Time Delivery Rate of all 10 distribution centers?

1.04 percentage points

0.39 percentage points

1.69 percentage points

0.56 percentage points

0.26 percentage points

Show answer & explanation

Answer: 1.04 percentage points

Answer

The median On-Time Delivery Rate of Zone East distribution centers exceeds the mean On-Time Delivery Rate of all 10 centers by 1.04 percentage points.

The mean of all 10 distribution centers is calculated by summing all on-time delivery rates (

938.1\%

) and dividing by 10 to get

93.81\%

. Filtering for Zone East gives 6 centers with delivery rates

[89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%]

. Because

N = 6

is even, the median is the average of the 3rd (

94.2\%

) and 4th (

95.5\%

) terms, yielding

94.85\%

. Subtracting

93.81\%

from

94.85\%

gives

1.04

percentage points.

Step-by-Step Solution

1

Calculate the mean On-Time Delivery Rate for all 10 distribution centers.

Sum of all delivery rates =

94.2 + 91.5 + 96.8 + 89.0 + 93.4 + 98.1 + 92.0 + 95.5 + 95.0 + 92.6 = 938.1\%

. Mean =

\frac{938.1}{10} = 93.81\%

.

To establish the overall average delivery performance benchmark across all facilities.

2

Filter the dataset to isolate the distribution centers in Zone East.

Zone East consists of 6 centers: H-1 (

94.2\%

), H-3 (

96.8\%

), H-4 (

89.0\%

), H-6 (

98.1\%

), H-8 (

95.5\%

), and H-10 (

92.6\%

).

The question specifically requires evaluating the median of the Zone East subset.

3

Sort the Zone East On-Time Delivery Rates in ascending order.

Sorted list of 6 values:

[89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%]

.

Sorting is a mandatory prerequisite step before determining the median of any dataset.

4

Calculate the median of the even-count (N = 6) Zone East subset.

The two central values (3rd and 4th) are

94.2\%

and

95.5\%

. Median =

\frac{94.2 + 95.5}{2} = 94.85\%

.

For an even number of elements, the median is defined as the exact arithmetic mean of the two middle elements.

5

Compute the difference between the calculated median and mean.

94.85\% - 93.81\% = 1.04

percentage points.

To answer the specific target question regarding the margin by which the median exceeds the mean.

Key Concept

Descriptive Statistics Interpretation from Tabular Subsets

Question 5Question →

The table below provides operational metrics for 10 international clinical trial sites participating in a multi-center biopharmaceutical study:

Site ID	Therapeutic Area	Patients Enrolled	Drop-out Rate (%)	Average Treatment Duration (Days)
Site A	Oncology	42	12.5	180
Site B	Immunology	56	8.0	120
Site C	Oncology	30	15.0	225
Site D	Neurology	64	6.25	90
Site E	Oncology	78	10.0	150
Site F	Immunology	48	12.5	135
Site G	Oncology	50	14.0	165
Site H	Neurology	32	9.375	105
Site I	Oncology	60	5.0	195
Site J	Immunology	40	10.0	150

Statement: For the subset of clinical trial sites with a drop-out rate of at least 10.0%, the median Average Treatment Duration exceeds the median Patients Enrolled by more than 110 days.

True

False

Show answer & explanation

Answer: True

Answer

True. The median Average Treatment Duration for the filtered subset of 6 sites is 157.5 days, and the median Patients Enrolled is 45 patients. The difference of 112.5 days exceeds 110 days.

The statement is correct (True) because filtering for sites with a drop-out rate of at least

10.0\%

yields exactly 6 sites. The median of Patients Enrolled across these 6 sites is

\frac{42+48}{2} = 45

, and the median of Average Treatment Duration is

\frac{150+165}{2} = 157.5

. The difference

157.5 - 45 = 112.5

is strictly greater than 110.

Step-by-Step Solution

1

Filter the dataset by the given condition

Subset consists of 6 sites with Drop-out Rate

\ge 10.0\%

: Site A, Site C, Site E, Site F, Site G, and Site J.

Only sites meeting the threshold of

\ge 10.0\%

drop-out rate must be analyzed.

2

Determine the median of Patients Enrolled for the filtered subset

Ordered values:

30, 40, 42, 48, 50, 78

. Median =

\frac{42 + 48}{2} = 45

.

Because the subset size

N = 6

is even, the median is the arithmetic mean of the two middle elements (3rd and 4th).

3

Determine the median of Average Treatment Duration for the filtered subset

Ordered values:

135, 150, 150, 165, 180, 225

. Median =

\frac{150 + 165}{2} = 157.5

.

Because

N = 6

is even, the median is the arithmetic mean of the 3rd and 4th ordered values.

4

Calculate the difference between the two medians and evaluate the statement

Difference =

157.5 - 45 = 112.5

days, which is greater than 110 days.

Since

112.5 > 110

, the statement is True.

Key Concept

Descriptive Statistics Interpretation on Filtered Even-Count Subsets

Question 6Question →

The table below details performance and financial metrics for 10 municipal express bus routes operated by a regional transit authority:

Route ID	Zone Type	Daily Ridership (Thousands)	On-Time Performance (%)	Operating Cost per Passenger ($)
Route U1	Urban Core	$14.2$	$82.5\%$	$3.40$
Route U2	Urban Core	$18.5$	$76.0\%$	$2.90$
Route U3	Urban Core	$22.0$	$88.0\%$	$4.10$
Route U4	Urban Core	$11.0$	$91.5\%$	$3.70$
Route U5	Urban Core	$16.4$	$79.0\%$	$2.50$
Route U6	Urban Core	$25.1$	$84.0\%$	$4.80$
Route S1	Suburban	$8.2$	$94.0\%$	$5.20$
Route S2	Suburban	$6.5$	$92.5\%$	$5.80$
Route S3	Suburban	$9.0$	$89.0\%$	$4.90$
Route S4	Suburban	$5.4$	$95.5\%$	$6.10$

Based on the table, what is the median Operating Cost per Passenger ($) for the express bus routes operating in the Urban Core zone?

3.40

3.55

3.57

3.70

3.90

Show answer & explanation

Answer: $3.55$

Answer

The median Operating Cost per Passenger for the Urban Core routes is $3.55.

Filtering the table for 'Urban Core' yields 6 routes. Sorting their Operating Cost per Passenger in ascending order gives:

2.50,

2.90,

3.40,

3.70,

4.10, and

4.80. Because there is an even number of items (6), the median is the arithmetic average of the middle two values (

3.40 and

3.70), which equals $3.55.

Step-by-Step Solution

1

Filter the table data for routes located in the 'Urban Core' Zone Type.

Identified 6 Urban Core routes: Route U1 (

3.40), Route U2 (

2.90), Route U3 (

4.10), Route U4 (

3.70), Route U5 (

2.50), and Route U6 (

4.80).

The question specifies finding descriptive statistics exclusively for the Urban Core zone routes.

2

Order the Operating Cost per Passenger values of the filtered Urban Core routes from least to greatest.

Sorted list of costs:

2.50,

2.90,

3.40,

3.70,

4.10,

4.80.

Finding a median requires ascending or descending order of values.

3

Calculate the median for the even dataset size (

N = 6

).

The two central values are the 3rd (

3.40) and 4th (

3.70) elements. Median =

\frac{\$3.40 + \$3.70}{2} = \$3.55

.

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 (Median of Filtered Even-Count Datasets)

Question 7Question →

The table below presents quarterly operational metrics for 10 semiconductor fabrication plants:

Plant ID	Region	Wafer Size	Defect Density (defects/cm²)	Operational Yield (%)
Fab 101	Asia-Pacific	300 mm	1.8	94.2
Fab 102	Asia-Pacific	300 mm	2.4	92.6
Fab 103	Asia-Pacific	300 mm	3.1	89.5
Fab 104	Asia-Pacific	300 mm	3.7	88.0
Fab 105	Asia-Pacific	300 mm	4.3	86.4
Fab 106	Asia-Pacific	300 mm	5.1	83.1
Fab 107	North America	300 mm	2.2	93.0
Fab 108	North America	200 mm	4.8	85.0
Fab 109	Europe	300 mm	3.5	87.5
Fab 110	Europe	200 mm	5.5	81.0

Statement: For semiconductor fabrication plants with a $300\text{ mm}$ wafer size located in the Asia-Pacific region, the median defect density is greater than $3.3\text{ defects/cm}^2$ .

True

False

Show answer & explanation

Answer: True

Answer

True

The correct response is True because the filtered subset of 6 plants in the Asia-Pacific region with 300 mm wafer sizes has defect densities of 1.8, 2.4, 3.1, 3.7, 4.3, and 5.1 defects/cm². Averaging the two middle values (3.1 and 3.7) yields a median of 3.4 defects/cm², which exceeds 3.3 defects/cm².

Step-by-Step Solution

1

Filter the dataset according to specified criteria

Identified 6 relevant plants: Fab 101, Fab 102, Fab 103, Fab 104, Fab 105, and Fab 106 (Region = Asia-Pacific AND Wafer Size = 300 mm).

The question requires analyzing descriptive statistics specifically for 300 mm wafer plants in the Asia-Pacific region.

2

Extract and sort the defect density data for the filtered subset

Sorted list of defect densities (

N = 6

):

1.8, 2.4, 3.1, 3.7, 4.3, 5.1

.

Calculating a median requires arranging the data points in ascending order.

3

Calculate the median of the even-count dataset

The 3rd element is

3.1

and the 4th element is

3.7

. The median is

\frac{3.1 + 3.7}{2} = 3.4\text{ defects/cm}^2

.

When

N

is even, the median is defined as the mean of the two middle numbers at positions

\frac{N}{2}

and

\frac{N}{2} + 1

.

4

Evaluate the statement

The calculated median of

3.4\text{ defects/cm}^2

is strictly greater than

3.3\text{ defects/cm}^2

. Therefore, the statement is True.

Comparing the calculated value (

3.4

) directly against the threshold in the stem (

3.3

) confirms the statement.

Key Concept

Descriptive Statistics Interpretation (Median of Even-Count Subsets)

Question 8Question →

The table lists performance and cost metrics for 10 municipal water treatment facilities during the 2025 fiscal year:

Facility ID	Region	Daily Capacity (MGD)	Average Turbidity (NTU)	Operating Cost ($/thousand gallons)
W-01	North	24.0	0.12	1.42
W-02	South	18.0	0.25	1.85
W-03	North	32.0	0.08	1.28
W-04	Central	12.0	0.19	1.65
W-05	South	28.0	0.15	1.56
W-06	Central	40.0	0.10	1.18
W-07	North	15.0	0.22	1.70
W-08	South	22.0	0.14	1.50
W-09	Central	35.0	0.11	1.34
W-10	North	10.0	0.28	1.92

Based on the data provided, what is the median operating cost, in dollars per thousand gallons, for the facilities that have a daily capacity greater than 20.0 MGD?

Show answer & explanation

Answer: 1.38

Answer

The median operating cost for facilities with a daily capacity greater than 20.0 MGD is $1.38 per thousand gallons.

Filtering the table for facilities with Daily Capacity > 20.0 MGD yields 6 facilities (W-01, W-03, W-05, W-06, W-08, W-09). Sorting their operating costs in ascending order produces:

1.18,

1.28,

1.34,

1.42,

1.50,

1.56. Because the count of elements is even (6), the median is the average of the 3rd element (

1.34) and the 4th element (

1.42), which equals $1.38.

Step-by-Step Solution

1

Filter the dataset by the given capacity constraint.

Identified 6 facilities with Daily Capacity > 20.0 MGD: W-01 (24.0 MGD), W-03 (32.0 MGD), W-05 (28.0 MGD), W-06 (40.0 MGD), W-08 (22.0 MGD), and W-09 (35.0 MGD).

Only facilities meeting the criterion 'Daily Capacity > 20.0 MGD' must be evaluated.

2

Extract and order the operating costs for the filtered subset.

Operating costs in ascending order:

1.18,

1.28,

1.34,

1.42,

1.50,

1.56.

Determining the median of a dataset requires arranging values sequentially.

3

Calculate the median for an even-numbered dataset.

Average of the 3rd and 4th values: $\frac{1.34 + 1.42}{2} = 1.38$.

When a dataset contains an even number of elements $N = 6$, the median is the arithmetic mean of the two central numbers at positions $N/2 = 3$ and $N/2 + 1 = 4$.

Key Concept

Calculating the median of a filtered even-count subset from tabular data.

Alternative Method

As a verification step, sum all operating costs in the filtered set:

1.18 + 1.28 + 1.34 + 1.42 + 1.50 + 1.56 = 8.28

. The mean is

8.28 / 6 = 1.38

. In this symmetric subset, the mean and median coincide at

1.38

.

Estimated Time:2m 0s

Question 9Question →

The table below details operational metrics for 10 wind turbines managed by a renewable energy utility during the previous calendar year:

Turbine ID	Region	Capacity (MW)	Availability (%)	Unplanned Maintenance (hours)
T-01	Offshore	6.0	94.2	48
T-02	Onshore	4.0	97.5	18
T-03	Offshore	8.0	91.0	84
T-04	Onshore	3.5	98.1	12
T-05	Offshore	6.0	95.8	36
T-06	Offshore	8.0	93.5	62
T-07	Onshore	4.0	96.0	24
T-08	Offshore	6.0	92.4	70
T-09	Onshore	3.5	98.8	8
T-10	Offshore	8.0	96.5	28

Based on the table, what is the median number of unplanned maintenance hours for turbines located in the Offshore region?

Show answer & explanation

Answer: 55

Answer

The median number of unplanned maintenance hours for turbines in the Offshore region is 55 hours.

Filtering the table for Offshore turbines yields 6 entries with unplanned maintenance hours of 48, 84, 36, 62, 70, and 28. Arranging these values in ascending order gives {28, 36, 48, 62, 70, 84}. Because the count is even (N = 6), the median is the average of the 3rd and 4th elements: (48 + 62) / 2 = 55 hours.

Step-by-Step Solution

1

Filter the dataset by Region

Identified 6 turbines in the Offshore region: T-01 (48 hrs), T-03 (84 hrs), T-05 (36 hrs), T-06 (62 hrs), T-08 (70 hrs), and T-10 (28 hrs).

The question specifically restricts the calculation to turbines operating in the Offshore region.

2

Sort the filtered unplanned maintenance hours in ascending order

Ordered set: 28, 36, 48, 62, 70, 84.

Finding the median requires data elements to be arranged sequentially.

3

Calculate the median of the even-count dataset (N = 6)

The two middle values are the 3rd element (48) and the 4th element (62). Mean = (48 + 62) / 2 = 55.

When a dataset contains an even number of observations, the median is the arithmetic average of the two central terms.

Key Concept

Descriptive Statistics Interpretation (Median of Even-Count Filtered Subsets)

Estimated Time:1m 30s

Question 10Question →

The table below provides operational performance metrics for 10 electric vehicle (EV) charging hubs operated by a regional clean energy authority during the second quarter of 2026:

Hub ID	Region	Fast Chargers	Daily Utilization Rate (%)	Average Session Duration (min)
H-101	North	12	72%	28.5
H-102	Metro	16	81%	42.0
H-103	South	8	58%	35.0
H-104	Metro	10	68%	31.0
H-105	Metro	14	88%	46.5
H-106	West	6	62%	22.0
H-107	Metro	20	75%	38.0
H-108	North	10	70%	44.0
H-109	Metro	8	74%	34.0
H-110	Metro	12	76%	52.0

What is the median Average Session Duration, in minutes, for the subset of charging hubs with a Daily Utilization Rate exceeding 71%?

38.0

40.0

42.0

42.25

40.17

Show answer & explanation

Answer: 40.0

Answer

40.0 minutes

Filtering the table for hubs with a Daily Utilization Rate strictly greater than 71% yields exactly 6 hubs: H-101 (28.5 min), H-102 (42.0 min), H-105 (46.5 min), H-107 (38.0 min), H-109 (34.0 min), and H-110 (52.0 min). Arranging these 6 duration values in ascending order gives: 28.5, 34.0, 38.0, 42.0, 46.5, 52.0. Because the dataset contains an even number of values (6), the median is calculated by averaging the middle two values: (38.0 + 42.0) / 2 = 40.0 minutes.

Step-by-Step Solution

1

Filter the table rows by the condition: Daily Utilization Rate > 71%.

Six hubs meet the threshold: H-101 (72%), H-102 (81%), H-105 (88%), H-107 (75%), H-109 (74%), and H-110 (76%).

Filtering isolates the relevant subset of hubs specified in the question stem.

2

Extract and order the Average Session Duration values for these 6 hubs in ascending numerical order.

Ordered values: 28.5, 34.0, 38.0, 42.0, 46.5, 52.0.

To determine a median, the data points must be arranged sequentially.

3

Calculate the median for an even dataset size (

N = 6

).

Median =

\frac{38.0 + 42.0}{2} = 40.0

minutes.

When

N

is even, the median is the arithmetic mean of the

\frac{N}{2}

-th element (3rd element = 38.0) and the

(\frac{N}{2} + 1)

-th element (4th element = 42.0).

Key Concept

Descriptive Statistics Interpretation

Question 11Question →

The table below lists key operational and financial metrics for 10 enterprise data center facilities operated by a global cloud services provider:

Facility ID	Tier Classification	Server Racks	Power Usage Effectiveness (PUE)	Monthly Maintenance Cost ($ in thousands)
Facility A	Tier III	450	1.35	64
Facility B	Tier IV	600	1.20	94
Facility C	Tier III	520	1.48	78
Facility D	Tier III	480	1.42	72
Facility E	Tier II	300	1.65	40
Facility F	Tier III	400	1.30	52
Facility G	Tier III	550	1.55	86
Facility H	Tier IV	650	1.25	98
Facility I	Tier III	460	1.38	68
Facility J	Tier II	350	1.60	82

Based on the table, what is the median monthly maintenance cost for the subset of facilities classified as Tier III?

$62,000

$68,000

$70,000

$72,000

$75,000

Show answer & explanation

Answer: $70,000

Answer

The median monthly maintenance cost for Tier III facilities is $70,000.

To find the median monthly maintenance cost of Tier III facilities, first isolate the 6 relevant rows: Facility A (

64k), Facility C (

78k), Facility D (

72k), Facility F (

52k), Facility G (

86k), and Facility I (

68k). Sorting these costs from lowest to highest yields:

52,000,

64,000,

68,000,

72,000,

78,000,

86,000. Because there are 6 values (an even count), the median is the average of the 3rd (

68,000) and 4th (

72,000) terms.

\frac{68,000 + 72,000}{2} = 70,000

. Therefore, $70,000 is the correct answer.

Step-by-Step Solution

1

Filter the table data for facilities classified as 'Tier III'.

Six facilities match this condition: Facility A (

64k), Facility C (

78k), Facility D (

72k), Facility F (

52k), Facility G (

86k), and Facility I (

68k).

The question specifically targets the subset of facilities with Tier III classification.

2

Sort the monthly maintenance costs for the filtered Tier III facilities in ascending numerical order.

52,000,

64,000,

68,000,

72,000,

78,000,

86,000.

Determining percentile or rank statistics such as the median requires ordering data from smallest to largest.

3

Calculate the median for this even-count dataset (N = 6).

Average of the 3rd value (

68,000) and 4th value (

72,000):

\frac{68,000 + 72,000}{2} = 70,000

.

When a dataset contains an even number of observations, the median is the arithmetic mean of the two middle terms.

Key Concept

Descriptive Statistics Interpretation (Even-Count Filtered Median)

Question 12Question →

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

Property ID	Building Grade	Leasable Area (sq ft)	Occupancy Rate (%)	Energy Intensity (kWh/sq ft)
P-101	Class A	120,000	92%	18.4
P-102	Class B	85,000	88%	22.1
P-103	Class A	210,000	95%	14.8
P-104	Class A	165,000	84%	19.2
P-105	Class B	95,000	91%	24.5
P-106	Class A	140,000	96%	16.0
P-107	Class B	110,000	79%	21.0
P-108	Class A	180,000	90%	15.6
P-109	Class A	250,000	89%	17.2
P-110	Class B	75,000	94%	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%?

Show answer & explanation

Answer: 17.2

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=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

\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=6

)

The 3rd value is 16.0 and the 4th value is 18.4. The median is

\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.

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