Q.71 The square root of the variance is known as –
1. Standard Error (SE)
2. Standard deviation (SD)
3. Standardized coefficients (SC)
4. Protective odds ratio
Square Root of Variance: Standard Deviation Defined
The square root of the variance is the standard deviation (SD), making option 2 correct.
Statistical Dispersion Measures
Variance quantifies data spread as average squared deviations from mean (units2), while standard deviation returns to original units via square root for intuitive interpretation.
Formula: σ = √variance = √[∑(xi – μ)2/N]
SD expresses typical deviation magnitude, crucial for normal distribution analysis (68-95-99.7 rule).
Correct Answer: Option 2
Standard deviation (SD) is mathematically defined as variance’s square root, measuring data dispersion in original units.
| Option | Term | Definition | Relation to Variance |
|---|---|---|---|
| 1 | Standard Error (SE) | Sample mean’s standard deviation: SE = SD/√n | Derived from SD, not sqrt(variance) directly |
| 2 | Standard Deviation (SD) | √Variance | Exact definition |
| 3 | Standardized Coefficients (SC) | Regression beta weights (unitless) | No variance relation |
| 4 | Protective Odds Ratio | Epidemiology: OR < 1 (risk reduction) | Logistic regression metric |
Option Explanations
- Option 1 (Incorrect): SE estimates population parameter precision; SE = SD/√n—requires SD first.
- Option 2 (Correct): Universal definition across statistics/biostatistics—√variance = SD.
- Option 3 (Incorrect): SC compares predictor strengths in multiple regression; standardized by SD ratios.
- Option 4 (Incorrect): Odds ratio measures association strength; “protective” when OR<1—no variance connection.
Practical Example
| Data: | 2, 4, 6, 8, 10 |
| Mean: | 6 |
| Variance: | 8 |
| SD = √8 ≈ 2.83 | (tells “typical deviation = 2.83 units”) |
| SE (n=5) = 2.83/√5 ≈ 1.27 |
NEET Biostatistics Essential
SD interprets variability magnitude; SE assesses sampling reliability. Remembering “√variance = SD” distinguishes from SE confusion—crucial for NEET medical statistics.
