Which one of the following statements is true?

Question

Question

This question was previously asked in

UGC NET Paper 2: Commerce 4th March 2023 Shift 1

Answer 1

The correct answer is For a symmetrical distribution β1 = 0.

Key Points

For a symmetrical distribution, the coefficient of skewness (skewness) is expected to be zero. Skewness measures the lack of symmetry or departure from symmetry in a distribution. A skewness of zero indicates that the distribution is perfectly symmetrical, with equal proportions of data on both sides of the mean.
Kurtosis measures the "peakedness" or flatness of distribution, not directly related to symmetry. A kurtosis value of zero represents a normal distribution (mesokurtic), where the distribution has a similar peak as the normal bell-shaped curve. Positive kurtosis (leptokurtic) indicates a distribution with a relatively sharper peak and heavier tails, while negative kurtosis (platykurtic) indicates a distribution with a flatter peak and lighter tails.

To summarize:

Skewness measures the lack of symmetry in a distribution. A skewness of zero indicates perfect symmetry.
Kurtosis measures the peakedness or flatness of a distribution, not directly related to symmetry. A kurtosis value of zero represents a normal distribution.