Which two of the following statements are true?

(A) Skewness studies the flatness or peakedness of the distribution

(B) A positively skewed distribution curve is stretched more to the right than to the left

(C) On the basis of empirical relationship between mean, mode, and median for moderately asymmetrical distribution, Karl Pearson's coefficient of skewness can be measured by 3 (Mean Median) divided by Standard Deviation

(D) If mean < mode, the distribution is positively skewed

Choose the correct option from those below:

Correct option is B

Which two of the following statements are true?
· Statement (A): False Skewness measures asymmetry, not flatness or peakedness. Flatness or peakedness is studied under kurtosis.
· Statement (B): True A positively skewed distribution curve has a longer tail on the right, indicating that most values are concentrated on the left side, with a few extreme values on the right.
· Statement (C): True Karl Pearson's coefficient of skewness is calculated using:

This formula applies to moderately asymmetrical distributions.
· Statement (D): False If mean < mode, the distribution is negatively skewed, not positively. A positively skewed distribution has the mean > mode.
Information Booster:
1. Positively Skewed Distribution:
· Characteristics: Long tail on the right, mean > median > mode.
· Common in cases like income distribution, where a few individuals earn significantly more than the majority.
2. Karl Pearson's Coefficient of Skewness:
· It provides a standardized measure of skewness. Positive values indicate positive skewness, while negative values indicate negative skewness.
Additional Knowledge:
1. Statement (A): Kurtosis vs. Skewness
· Kurtosis: Describes the "tailedness" of the distribution. Flat (platykurtic), normal (mesokurtic), and peaked (leptokurtic).
· Skewness: Measures asymmetry.
2. Statement (D): Mean < Mode Relationship
· If Mean < Median < Mode, it is a negatively skewed distribution.