Which of the following measures of skewness is based on the distance of upper and lower quartiles from the median value in a dataset?

Correct option is C

Bowley's Coefficient of Skewness measures the asymmetry of a distribution by evaluating the distances between the quartiles and the median. Specifically, it is calculated using the formula:

Where:
· Q1 is the lower quartile,
· Q2 is the median, and
· Q3 is the upper quartile.
This formula quantifies skewness by comparing the interquartile range with the distance of the quartiles from the median, effectively measuring how evenly the data is distributed around the median.
Information Booster:
· Skewness: It describes the degree of asymmetry of a distribution around its mean.
· Quartiles: Quartiles divide a dataset into four equal parts, giving insights into the distribution of values.
· Median: The median is a measure of central tendency that is less affected by outliers compared to the mean.
· Symmetric Distribution: A distribution is symmetric if it has equal quartiles and the mean equals the median.
· Positive Skewness: Occurs when the right tail (higher values) is longer or fatter than the left.
· Negative Skewness: Occurs when the left tail (lower values) is longer or fatter than the right.
Additional Information:
· Karl Pearson's Coefficient of Skewness: Based on moments about the mean, not quartiles.
· Kelly's Measure of Skewness: Similar to Bowley's but calculated differently and focuses on mean and median.
· Coefficient of Skewness based on moments: Utilizes the mean and standard deviation to calculate skewness, focusing on the data's dispersion.