MP Board · Class 11 · Mathematics · StatisticsIf each observation of a data set is multiplied by 2, then the standard deviation of the new data set:
Step-by-Step Solution
Standard deviation is affected by change of scale. If each observation is multiplied by a non-zero constant k, the new standard deviation becomes |k| times the original standard deviation. Here k = 2, so the standard deviation is multiplied by 2.
Detailed Options Breakdown
Option : Remains unchanged
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Statistics.
Option 1: Is doubled (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: Is quadrupled
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Statistics.
Option 3: Is halved
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Statistics.
💡 Study Guide: This question tests core syllabus concepts from Statistics. For formulas, key summaries, and mock exam reference guides, read the full Statistics Revision Notes.