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📐 Mathematics  ·  Statistics  ·  JEE

If every observation in a data set is increased by 5, the variance:

Answer: remains unchanged.

  • A increases by 5
  • B increases by 25
  • C remains unchanged
  • D increases by 10

Correct answer: C. remains unchanged

Explanation: Adding a constant shifts the data without changing spread, so the variance is unchanged.

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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