The table below presents operating metrics for 10 regional micro-grid stations during an annual monitoring period: | Station ID | Elevation (m) | Solar Irradiance (kWh/m²) | Wind Capacity Factor (%) | Battery Degradation Rate (%/yr) | System Efficiency (%) | |---|---|---|---|---|---| | ST-01 | 150 |

The table below presents operating metrics for 10 regional micro-grid stations during an a… — GMAT

The table below presents operating metrics for 10 regional micro-grid stations during an annual monitoring period:

Station ID	Elevation (m)	Solar Irradiance (kWh/m²)	Wind Capacity Factor (%)	Battery Degradation Rate (%/yr)	System Efficiency (%)
ST-01	150	5.8	32	3.4	84
ST-02	320	5.5	38	3.1	82
ST-03	480	5.2	41	2.8	85
ST-04	610	4.9	45	2.5	81
ST-05	750	5.1	49	2.2	87
ST-06	890	4.3	52	1.9	83
ST-07	1040	4.0	56	1.7	88
ST-08	1180	3.7	60	1.4	86
ST-09	1350	3.4	64	1.1	89
ST-10	1500	3.1	68	0.8	91

Evaluate the following statement based on the data provided:

'When all 10 stations are ordered by increasing Elevation, there is a strictly monotonic inverse relationship between Elevation and Solar Irradiance.'

Cevap: Cevap

Cevap

False. The relationship between Elevation and Solar Irradiance is not strictly monotonic because Solar Irradiance increases from ST-04 to ST-05.

The evaluated statement claims a strictly monotonic inverse relationship between Elevation and Solar Irradiance. Checking the values sequentially by increasing elevation shows that Solar Irradiance decreases from ST-01 (

5.8

) through ST-04 (

4.9

), but increases at ST-05 (

5.1

). Consequently, the relationship is not strictly monotonic.

Adım Adım Çözüm

Verify table ordering by Elevation

The table is already sorted in ascending order of Elevation from ST-01 (

150\text{ m}

) to ST-10 (

1500\text{ m}

To evaluate monotonicity across Elevation, we must inspect Solar Irradiance values sequentially from lowest to highest elevation.

Examine Solar Irradiance values sequentially

ST-01:

5.8

, ST-02:

5.5

, ST-03:

5.2

, ST-04:

4.9

, ST-05:

5.1

A strict inverse monotonic trend requires that every successive value be strictly smaller than the preceding value.

Identify non-monotonic exception

Between ST-04 and ST-05, Solar Irradiance increases from

4.9\text{ kWh/m}^2

5.1\text{ kWh/m}^2

Because

5.1 > 4.9

, there is a local increase, which invalidates a strict monotonic inverse correlation across the full dataset.

Anahtar Kavram

Evaluating strict monotonicity vs. general macro trends across sorted multi-column tables

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