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.

The table lists performance and cost metrics for 10 municipal water treatment facilities d… — GMAT

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?

Cevap: 1.38 $/thousand gallons

Cevap

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.

Adım Adım Çözüm

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.

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.

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 $N/2 + 1 = 4$.

Anahtar Kavram

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

Alternatif Yöntem

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

Tahmini Süre:2m 0s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Konular

Bu konudan daha fazla soru