To determine which column indicates both high precision and high accuracy, we need to compute two important metrics for each instrument's measurements:
1. Accuracy: This can be assessed using the Mean Absolute Error (MAE), which measures the average magnitude of the errors between the observed values and the actual value.
2. Precision: This is measured using the Standard Deviation, which indicates how much the values are spread out from their mean.
Given the actual value is 5.5, we use the following data:
- Instrument 1: [5.4, 5.7, 5.6, 5.7, 5.6]
- Instrument 2: [4.9, 6.2, 7.3, 5.1, 3.7]
- Instrument 3: [8.9, 4.1, 4.3, 9.2, 3.3]
- Instrument 4: [3.2, 2.9, 3.1, 3.1, 2.8]
### Calculating Metrics:
For Instrument 1:
- Mean Absolute Error (MAE): [tex]\( 0.13999999999999985 \)[/tex]
- Standard Deviation (SD): [tex]\( 0.10954451150103316 \)[/tex]
For Instrument 2:
- Mean Absolute Error (MAE): [tex]\( 1.06 \)[/tex]
- Standard Deviation (SD): [tex]\( 1.22245654319489 \)[/tex]
For Instrument 3:
- Mean Absolute Error (MAE): [tex]\( 2.38 \)[/tex]
- Standard Deviation (SD): [tex]\( 2.546841180757057 \)[/tex]
For Instrument 4:
- Mean Absolute Error (MAE): [tex]\( 2.48 \)[/tex]
- Standard Deviation (SD): [tex]\( 0.14696938456699082 \)[/tex]
### Comparing Metrics:
To determine which instrument has the highest accuracy, we look for the smallest MAE. Among the values provided:
- Instrument 1 has the smallest MAE [tex]\( 0.13999999999999985 \)[/tex].
To determine which instrument has the highest precision, we look for the smallest standard deviation. Among the values provided:
- Instrument 1 also has the smallest standard deviation [tex]\( 0.10954451150103316 \)[/tex].
### Conclusion:
Instrument 1 (Column 1) exhibits both the highest accuracy (smallest MAE) and the highest precision (smallest SD). Therefore, the answer is:
C. 1
