To determine whether the statement "Median is never larger than mean" is true or false, let's analyze the definitions and behaviors of the median and mean in different distributions:
1. Mean (Average): The mean is the sum of all values in a dataset divided by the number of values. It is a measure of central tendency that can be influenced by extreme values (outliers).
2. Median: The median is the middle value of a dataset when it is ordered from lowest to highest. If the dataset has an even number of values, the median is the average of the two middle values. The median is less sensitive to outliers compared to the mean.
To determine the validity of the statement, consider different scenarios:
- Symmetric Distributions: In a perfectly symmetric distribution (e.g., normal distribution), the mean and median are equal.
- Right-Skewed Distributions: In a right-skewed distribution (where the tail is on the right side), the mean is typically greater than the median because the mean is influenced by the higher tail values.
- Left-Skewed Distributions: In a left-skewed distribution (where the tail is on the left side), the mean is typically less than the median because the mean is influenced by the lower tail values.
Given these scenarios:
- In right-skewed distributions, the median can indeed be less than the mean.
- In left-skewed distributions, the median can be greater than the mean.
Thus, it is possible for the median to be larger than the mean.
Therefore, the claim that "Median is never larger than mean" is False.
