is the mean or median a better estimate for the parameter of interest?
To determine whether the mean or median is a better estimate for the parameter of interest, you need to consider the characteristics of the data and the goal of your analysis.
The mean is the average value of a dataset and is calculated by summing all the values and dividing by the total number of observations. It is sensitive to extreme values or outliers since it directly incorporates every data point. The mean is often used when the data is normally distributed and there are no significant outliers.
On the other hand, the median is the middle value of a dataset when arranged in ascending or descending order. It is less affected by outliers since it only considers the central value and ignores extreme values. The median is preferred when the data contains outliers or is skewed, as it provides a more robust estimate.
If your objective is to have a summary statistic that represents the typical value or central tendency of the data, then the mean is generally appropriate. Conversely, if your goal is to estimate the value that separates the higher half from the lower half of the data, or if you have skewed data or outliers, then the median would be a better choice.
In conclusion, the decision of whether to use the mean or median as the better estimate depends on the nature of the data, the presence of outliers, and the specific objective of your analysis.