Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
Consider the data set 14, 18, 14, 14, 10, 29, 33, 31, 25. If you add 20 to each of the values, then
(A) both mean and variance change (B) both mean and variance are unchanged
(C) the mean is unchanged, variance changes (D) the mean changes, the variance is unchanged
Options:
(A) both mean and variance change
(B) both mean and variance are unchanged
(C) the mean is unchanged, variance changes
(D) the mean changes, the variance is unchanged
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2012 Q.45)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"Consider the data set 14, 18, 14, 14, 10, 29, 33, 31, 25. If you add 20 to each of the values, then..."*
- **Option (D) [CORRECT]**: *"the mean changes, the variance is unchanged"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"both mean and variance change"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (B) [INCORRECT]**: *"both mean and variance are unchanged"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"the mean is unchanged, variance changes"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **D**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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