Question:
For a given sample the computed values of variance and fourth central moment are \(3\) and \(63\) respectively. Then underlying frequency distribution is classified as:
For a given sample the computed values of variance and fourth central moment are \(3\) and \(63\) respectively. Then underlying frequency distribution is classified as:
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If \(\beta_2>3\): Leptokurtic.
If \(\beta_2=3\): Mesokurtic (Normal).
If \(\beta_2<3\): Platykurtic.
If \(\beta_2=3\): Mesokurtic (Normal).
If \(\beta_2<3\): Platykurtic.
Updated On: Jun 11, 2026
- Leptokurtic
- Mesokurtic
- Platykurtic
- Normal
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The Correct Option is A
Solution and Explanation
Step 1: Compute coefficient of kurtosis.
Variance, \[ \mu_2=3. \] Fourth central moment, \[ \mu_4=63. \] Coefficient of kurtosis, \[ \beta_2 = \frac{\mu_4}{\mu_2^2}. \] Substituting, \[ \beta_2 = \frac{63}{3^2} = \frac{63}{9} = 7. \]
Step 2: Classify the distribution.
For normal distribution, \[ \beta_2=3. \] Here, \[ \beta_2=7>3. \] Therefore the distribution is \[ \boxed{\text{Leptokurtic}}. \]
Variance, \[ \mu_2=3. \] Fourth central moment, \[ \mu_4=63. \] Coefficient of kurtosis, \[ \beta_2 = \frac{\mu_4}{\mu_2^2}. \] Substituting, \[ \beta_2 = \frac{63}{3^2} = \frac{63}{9} = 7. \]
Step 2: Classify the distribution.
For normal distribution, \[ \beta_2=3. \] Here, \[ \beta_2=7>3. \] Therefore the distribution is \[ \boxed{\text{Leptokurtic}}. \]
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