Question:
Which one of the following is mathematical notation for precision? [where $\sigma$ is standard deviation]
Which one of the following is mathematical notation for precision? [where $\sigma$ is standard deviation]
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Think of it this way: Precision is the opposite of Spread. Therefore, $\sigma$ (the spread) must always be in the denominator of a precision formula.
Updated On: May 20, 2026
- $\sqrt{2} \times \sigma$
- $\frac{1}{\sqrt{2} \times \sigma}$
- $0.67 \times \sigma$
- $\frac{1}{0.67 \times \sigma}$
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The Correct Option is B
Solution and Explanation
Concept:
In statistics and measurement theory, "precision" refers to the consistency or repeatability of measurements. It is inversely related to the spread of the data, which is represented by the standard deviation ($\sigma$).
Step 1: Defining Precision mathematically.
Precision is defined as the reciprocal of the measure of dispersion. In the context of the normal distribution, the precision parameter $h$ is expressed in terms of the standard deviation $\sigma$.
Step 2: Relating Standard Deviation to Precision.
The formula for the precision of a normal distribution is: \[ h = \frac{1}{\sigma \sqrt{2}} \] This indicates that as the standard deviation increases (more spread/less consistency), the precision decreases. Conversely, a small standard deviation results in high precision.
Step 3: Conclusion.
Comparing the standard mathematical definition of precision to the options provided, Option (2) correctly identifies $\frac{1}{\sqrt{2} \times \sigma}$ as the notation.
Step 1: Defining Precision mathematically.
Precision is defined as the reciprocal of the measure of dispersion. In the context of the normal distribution, the precision parameter $h$ is expressed in terms of the standard deviation $\sigma$.
Step 2: Relating Standard Deviation to Precision.
The formula for the precision of a normal distribution is: \[ h = \frac{1}{\sigma \sqrt{2}} \] This indicates that as the standard deviation increases (more spread/less consistency), the precision decreases. Conversely, a small standard deviation results in high precision.
Step 3: Conclusion.
Comparing the standard mathematical definition of precision to the options provided, Option (2) correctly identifies $\frac{1}{\sqrt{2} \times \sigma}$ as the notation.
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