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📐 Mathematics  ·  Statistics  ·  JEE

Standard deviation measures:

Answer: Spread (variability) of data around the mean.

  • A The central tendency of the data, like the mean does
  • B Spread (variability) of data around the mean
  • C The middle value of the data when arranged in order
  • D The single largest value present in the data set

Correct answer: B. Spread (variability) of data around the mean

Explanation: Standard deviation measures how spread out values are from the mean. Higher SD = more spread.

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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