In a skewed distribution the mean and median will be at different locations in the distributionSelect one:TrueFalse

Answer

The statement is True.

In a skewed distribution, the mean and median will indeed occupy different positions due to the asymmetrical nature of the data distribution.

1. Understanding Skewness: A distribution is considered skewed if it is not symmetrical. In a positively skewed (or right-skewed) distribution, the tail on the right side is longer, and the mean is typically greater than the median. Conversely, in a negatively skewed (or left-skewed) distribution, the tail on the left side is longer, causing the mean to be less than the median.

2. Order of Measures:

   • In a right-skewed distribution, the sequence of the measures is: Median < Mean.
   • In a left-skewed distribution, the sequence is: Mean < Median.

This difference in position highlights how the mean is influenced by extreme values (or outliers) in one tail of the distribution, while the median remains a more robust measure, representing the middle value and less affected by outliers.

Thus, in any skewed distribution, the discrepancy between the mean and median is indicative of the skewness present in the data.