There are several kinds of mean in mathematics, especially in
statistics. Each mean serves to summarize a given group of data, often to better
understand the overall value (magnitude and sign) of a given data
set.
For a data set, the arithmetic mean, also known as “arithmetic average”, is a
measure of central tendency of a finite set of numbers: specifically, the sum of
the values divided by the number of values. The arithmetic mean of a set of
numbers x1, x2, …, xn is typically denoted using an overhead bar, If the data
set were based on a series of observations obtained by sampling from a
statistical population, the arithmetic mean is the sample mean to distinguish it
from the mean, or expected value, of the underlying distribution.
Outside probability and statistics, a wide range of other notions of mean are
often used in geometry and mathematical analysis; examples are given below. (資料分析 )
In descriptive statistics, the mean may be confused with the median,
mode or mid-range, as any of these may incorrectly be called an “average” (more
formally, a measure of central tendency). The mean of a set of observations is
the arithmetic average of the values; however, for skewed distributions, the
mean is not necessarily the same as the middle value (median), or the most
likely value (mode). For example, mean income is typically skewed upwards by a
small number of people with very large incomes, so that the majority have an
income lower than the mean. (資料分析 )
