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📐 Mathematics  ·  Statistics  ·  JEE

If adding a constant k to each observation, mean:

Answer: Increases by k.

  • A Remains the same
  • B Increases by k
  • C Multiplies by k
  • D Becomes 0

Correct answer: B. Increases by k

Explanation: Mean shifts by the constant. New mean = original mean + k.

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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