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📐 Mathematics  ·  Statistics  ·  JEE

In grouped data, the mode formula is:

Answer: l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h.

  • A l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h
  • B l + (n/2-F)/f × h
  • C Mean - Mode = 3(Mean-Median)
  • D sigma(fx)/n

Correct answer: A. l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h

Explanation: Mode (grouped) = l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h, where f₁ = modal class freq, f₀ = prev class freq, f₂ = next class freq.

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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