​$$\text{Which of the following are true for a mesokurtic curve?} \\\text{A. } \beta_2 = 3 \\\text{B. } \gamma_2 = 0 \\\text{C. } \beta_2 > 3 \\\text{D. } \beta_2 < 3 \\\text{E. } \gamma_2 = 3 \\\text{Choose the correct answer from the options given below:}$$​​

Correct option is A

· A. β₂ = 3: A mesokurtic curve has a kurtosis (β₂) equal to 3. This is characteristic of the normal distribution, which is neither too flat nor too peaked.
· B. γ₂ = 0: The skewness (γ₂) for a mesokurtic curve is 0. This indicates that the distribution is symmetrical, like the normal distribution.
Thus, the correct answer is (a) A and B only because both β₂ = 3 and γ₂ = 0 are true for a mesokurtic distribution.
Information Booster:
· Kurtosis (β₂) measures the "tailedness" of a distribution. For a mesokurtic distribution, the kurtosis is 3, indicating a normal level of peak and tails.
· Skewness (γ₂) measures the asymmetry of the distribution. A mesokurtic distribution (like the normal distribution) is perfectly symmetrical, so the skewness is 0.
· Leptokurtic distributions have kurtosis greater than 3, indicating sharper peaks and heavier tails, while platykurtic distributions have kurtosis less than 3, indicating flatter peaks and lighter tails.
Additional Knowledge - Incorrect Options:
(b) B and C only:
· C. β₂ > 3 is incorrect for mesokurtic distributions. β₂ > 3 would be characteristic of leptokurtic distributions, not mesokurtic.
(c) B and D only:
· D. β₂ < 3 is incorrect for mesokurtic distributions. β₂ < 3 would indicate a platykurtic distribution.
(d) D and E only:
· E. γ₂ = 3 is incorrect. For a mesokurtic (normal) distribution, γ₂ = 0, not 3.