Which statistic answers your question?
Where is the middle? The mean uses every value but is dragged by extremes; the median is the middle value and ignores how extreme the tails are. With skewed data such as incomes or reaction times, report the median. With roughly symmetric data, the mean is fine and connects to most later methods.
How spread out is it? The standard deviation is the typical distance from the mean. The interquartile range covers the middle half of the data and, like the median, shrugs off outliers.
Where does one value stand? A z-score counts standard deviations from the mean; a percentile says what share of the data sits below it.
Is a difference real? That is inference: confidence intervals, t-tests, chi-square tests and the p-values they produce.
The bean machine at the top of this page is Francis Galton’s 1889 demonstration of why so many measurements pile up into a bell: each bead makes many small, random left-or-right bounces, and the sum of lots of small random nudges tends toward a normal curve. That idea, the central limit theorem, is the reason the normal distribution shows up across this site. Galton knew people grasp a bell curve faster by watching beads fall than by reading a formula; ahaboo’s narrated explainers use the same trick on tax brackets, photosynthesis and the phases of the Moon.