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Skewness & Kurtosis — Previous Year Questions

📊 Topic Overview​

MetricValue
Papers Appeared7 of 27 (25.9%)
Priority🟡 MEDIUM
Section DistributionSec A: ~1
Most Repeated"Kurtosis (short note)" / "Skewness (short note)"
NoteHeavily overlaps with Divergence from Normality (which covers the same content more fully)

🎯 Must-Know Concepts​

  1. Skewness: measure of asymmetry; positive vs negative skew
  2. Kurtosis: measure of peakedness; leptokurtic, platykurtic, mesokurtic
  3. Effect of skewness on mean-median-mode relationship
  4. Diagrams for each type

🔥 Most Repeated Questions​

Common phrasings:

  • "Kurtosis (short note)."
  • "Skewness (short note)."
  • "What is skewness? Explain the factors causing divergence in normal distribution."
  • "Outliers and curvilinearity (short note)."

Skewness (Section C — ~100 words):​

Skewness is a measure of the asymmetry of a frequency distribution. A perfectly normal distribution has zero skewness.

Positive Skew (Right skew): The tail extends to the right; most scores cluster at the lower end. Mean > Median > Mode.

Negative Skew (Left skew): The tail extends to the left; most scores cluster at the higher end. Mean < Median < Mode.

Skewness can be caused by ceiling effects, floor effects, extreme outliers, or the natural properties of the variable being measured.

Kurtosis (Section C — ~100 words):​

Kurtosis is a measure of the peakedness (degree of flatness or pointedness) of a frequency distribution relative to the normal curve.

Leptokurtic: More peaked than normal; tall and narrow with heavier tails than a normal distribution. Excess kurtosis > 0.

Platykurtic: Flatter than normal; scores spread more evenly across the range. Excess kurtosis < 0.

Mesokurtic: Same peakedness as the normal distribution. Excess kurtosis = 0.

Kurtosis affects the reliability of statistical tests that assume normality — extreme kurtosis violates those assumptions.

Combined Answer for Section B (~250 words):​

Skewness and Kurtosis are two key ways in which empirical distributions diverge from the ideal normal curve.

Skewness measures asymmetry. When the left and right halves of the distribution are not mirror images, the distribution is skewed:

  • Positive skew: Long right tail. Mean is pulled toward the high scores: Mean > Median > Mode. Example: Income distribution (most people earn moderately, a few earn extremely high amounts).
  • Negative skew: Long left tail. Mean is pulled toward low scores: Mean < Median < Mode. Example: Age at death in developed countries (most die in old age, few die young).

Measuring Skewness: Pearson's coefficient of skewness = 3(Mean − Median) / SD. A value of 0 = symmetrical.

Kurtosis measures peakedness:

  • Leptokurtic: Tall, narrow peak; heavy tails. Scores are concentrated near the mean. Examples: distributions of test scores in homogeneous, well-trained groups.
  • Platykurtic: Flat, broad distribution; light tails. Scores are widely spread. Example: uniform distributions.
  • Mesokurtic: Normal kurtosis. The baseline against which others are compared.

Diagrams are essential: draw all three kurtosis types on one graph and both skew types clearly labelled.

Both skewness and kurtosis inform decisions about which statistical tests to use. Highly skewed or kurtotic data may require non-parametric tests or data transformation before applying parametric analyses.

🧠 Memory Aid​

Skewness: Tail direction = direction of skew. Mean gets pulled toward the tail.

Kurtosis (PLM):

  • Platykurtic = flat (low peak)
  • Leptokurtic = lean/tall (high peak)
  • Mesokurtic = matching normal

📚 Related Content​

✅ Self-Assessment​

  1. In a positively skewed distribution, which is largest — mean, median, or mode?
  2. What is the difference between leptokurtic and platykurtic?
  3. Write Pearson's formula for skewness.
  4. Draw labelled diagrams for positive skew and negative skew.
  5. What does zero kurtosis indicate?

💡 Exam Tips​

  • Section C (3 marks): Skewness = asymmetry → positive/negative with mean-median-mode order → Kurtosis = peakedness → three types. Add diagram if space allows.
  • Always draw the labelled diagrams — they differentiate good answers from average ones.
  • Skewness and Kurtosis are sub-components of the larger Divergence from Normality topic — prepare the full Divergence answer for Section A, and these as standalone Section C short notes.