The square root of the variance is?

Appeared in: ISRO- 2016

Explanation

Standard deviation is mathematically defined as the positive square root of the variance.
Variance measures the average squared difference of data points from the mean, so its units are squared (e.g., cm²).
Taking the square root to get the standard deviation returns the measure of spread to the original units (e.g., cm), making it easier to interpret in a practical context.

Option B: The standard error measures the variability or precision of a sample mean, not the variability of individual data points within the sample.
Option C: A Z-score is a standardized value that indicates how many standard deviations a single data point is from the mean. It describes position, not overall dataset spread.
Option D: Variance is the value before taking the square root. The question specifically asks for the square root of the variance.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Definition of Standard Deviation as background academic context rather than a clinical decision trigger.
In clinical research and practice, standard deviation is crucial for understanding the variability in patient data, such as blood pressure readings, lab values, or response to treatment.
A small standard deviation indicates that data points are clustered closely around the mean, suggesting high consistency or precision. A large standard deviation indicates that data points are spread out over a wider range.
What if? If a new drug trial reports that the mean reduction in cholesterol is 20 mg/dL with a small SD of 2 mg/dL, it implies the drug has a very consistent effect across patients. If the SD were large (e.g., 15 mg/dL), it would suggest the drug's effectiveness varies greatly from person to person.

How to Approach the Question

This is a direct recall question testing a fundamental definition in biostatistics.
Identify the key terms in the question: 'square root' and 'variance'.
Recall the mathematical relationship between the main measures of statistical dispersion.
Variance is the average of squared deviations from the mean. Standard Deviation (SD) is defined as the square root of the variance.
Evaluate the options based on this definition. 'Standard deviation' is the only option that directly matches the definition asked for in the question.

Concept Tested & Keywords

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E6 NursingResearch Polit 11e Part 1 p. 387-389

E6 NursingResearch Sukhpal Kaur p. 459-461

E6 NursingResearch Suresh Sharma 5e Part 2 p. 150-152

Practise the full ISRO- 2016

Attempt every question from this paper in a timed mock, then review the full solution for each one.