Most stable measure of central tendency

The mean is generally considered the most stable measure of central tendency. Here’s why:

1. Mathematical Precision: The mean uses all values in the dataset, which gives it a stable, balanced position as a true average.
2. Less Fluctuation: When multiple samples are taken from the same population, the mean tends to vary less across samples compared to other measures like the median or mode.
3. Suitability for Statistical Analysis: The mean is widely used in inferential statistics and many statistical tests (like t-tests and ANOVA) are based on it, which makes it reliable and preferred in many analyses.

However, stability here refers to the mean’s reliability across samples, not its resistance to outliers. When data contains extreme values, the median can be a more robust measure, as it’s less affected by outliers and skewed distributions.