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📐 Mathematics  ·  Statistics  ·  JEE

If the standard deviation of x₁, x₂, ..., xₙ is σ, the standard deviation of 3x₁, 3x₂, ..., 3xₙ is:

Answer: 3σ.

  • A σ
  • B
  • C
  • D σ/3

Correct answer: B. 3σ

Explanation: Scaling each observation by 3 scales the standard deviation by |3|, giving 3σ.

Normal Distribution: the 68-95-99.7 Rule68% within ±1σ95% within ±2σmean=median=mode (centre)

In a perfectly normal (bell-shaped) distribution, mean, median, and mode all coincide at the centre; about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 - the empirical rule used to judge how typical or extreme a value is.

Concept context

Mean, median, mode, standard deviation, and data interpretation

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