a histogram of a set of data indicates that the distribution of the data is skewed right. which measure of central tendency will likely be larger, the mean or the median? why?
For a distribution that is skewed right, the mean will be larger than the median.
Why the mean is larger
- A right-skewed (positively skewed) distribution has a long tail stretching to the right, with a few unusually large values.
- The mean uses every value in the data, so those large high-end values pull the mean to the right (upward), away from the bulk of the data.
- The median is just the middle value when the data are ordered, so extreme high values barely affect it.
- As a result, in a right-skewed distribution we typically have:
mode<median<mean\text{mode}<\text{median}<\text{mean}mode<median<mean.
So, the mean will likely be larger than the median because the right-side tail of large values pulls the mean upward more than it pulls the median.
Information gathered from public forums or data available on the internet and portrayed here.