If a distribution is skewed, should the mean must be smaller than the median?
Which way is it skewed? If the tail is to the right (positively skewed), the mean is greater. If the tail is to the left (negatively skewed), the mean is smaller. The mean is greatly effected by outliers.
Not necessarily. The relationship between the mean and the median in a skewed distribution depends on the direction and degree of the skewness.
Skewness refers to the asymmetry of a distribution. It measures the extent to which the data is biased towards one tail relative to the other. In a positively skewed distribution (also known as right-skewed), the tail on the right side is longer or fatter than the left tail. This means that the majority of the data is concentrated on the lower side of the distribution, with a few extreme values on the higher side.
In a positively skewed distribution, where the mean is likely to be larger than the median. The extreme values on the higher side pull the mean towards that tail, resulting in a higher value compared to the median. The median, on the other hand, is less affected by extreme values and provides a better representation of the central tendency of the data. Therefore, in a positively skewed distribution, the mean is typically greater than the median.
Conversely, in a negatively skewed distribution (also known as left-skewed), the tail on the left side is longer or fatter than the right tail. The majority of the data is concentrated on the higher side, with a few extreme values on the lower side. In this case, the mean is likely to be smaller than the median since the extreme values on the lower side pull the mean towards that tail.
However, it's important to note that the relationship between the mean and the median is not a strict rule. There can be situations where the mean is smaller than the median in a positively skewed distribution or larger than the median in a negatively skewed distribution. It all depends on the shape and specific characteristics of the data.
If a distribution is skewed, the mean does not have to be smaller than the median. The relationship between the mean and the median depends on the direction of the skewness.
1. Positive Skewness (right-skewed): In a right-skewed distribution, the tail of the distribution extends to the right, and the majority of the data points are located towards the lower end. In this case, the mean is typically greater than the median. The reason is that the presence of extreme values in the right tail of the distribution pulls the mean towards the larger values.
2. Negative Skewness (left-skewed): In a left-skewed distribution, the tail of the distribution extends to the left, and most of the data points are located towards the higher end. In this case, the mean is usually smaller than the median. The occurrence of extreme values in the left tail pulls the mean towards the smaller values.
It is important to note that the mean is sensitive to extreme values, whereas the median is not. Therefore, skewness can affect the relationship between the mean and the median in a distribution.