mean

mean, in statistics, a type of average. The arithmetic mean of a group of numbers is found by dividing their sum by the number of members in the group; e.g., the sum of the seven numbers 4, 5, 6, 9, 13, 14, and 19 is 70 so their mean is 70 divided by 7, or 10. Less often used is the geometric mean (for two quantities, the square root of their product; for n quantities, the nth root of their product).

In mathematics, two theorems, one associated with differential calculus and one with integral calculus. The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line connecting the endpoints of the function's graph on that interval. For example, if a car covers a mile from a dead stop in one minute, it must have been traveling exactly a mile a minute at some point along that mile. In integral calculus, the mean value of a function on an interval is, in essence, the arithmetic mean (see mean, median and mode) of its values over the interval. Because the number of values is infinite, a true arithmetic mean is not possible. The theorem shows how to find the mean value using a definite integral. Seealso Rolle's theorem.

Learn more about mean-value theorems with a free trial on Britannica.com.

In radioactivity, the average lifetime of all the nuclei of a particular unstable atomic species. This time interval is the sum of the lifetimes of all the individual unstable nuclei in a sample, divided by the total number of unstable nuclei present. It is the reciprocal of the decay constant. For a given isotope, the mean life is always 1.443 times its half-life. For example, lead-209 decays to bismuth-209 with a half-life of 3.25 hours and a mean life of 4.69 hours.

Learn more about mean life with a free trial on Britannica.com.

See Mean