Zaymiey

📐 Mathematics  ·  Statistics  ·  JEE

For grouped data, Pearson's first coefficient of skewness is:

Answer: 3(Mean - Median)/SD.

  • A (Mean - Mode)/SD
  • B (Mean - Median)/SD
  • C 3(Mean - Median)/SD
  • D (Median - Mode)/SD

Correct answer: C. 3(Mean - Median)/SD

Explanation: Pearson's first skewness = (Mean - Mode)/SD. For grouped data the mode is ill-defined, so the second formula 3(Mean - Median)/SD is used instead via the empirical relation Mode ≈ 3Median - 2Mean. Answer: 3(Mean - Median)/SD.

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

Read the full Statistics notes →