# Arithmetic mean

Luncat ka: pituduh, sungsi

Dina matematik jeung statistik, arithmetic mean tina susunan data nyaeta jumlah sakabeh anggota dibagi ku jumlah "item" dina eta susunan. (Kecap set digunakeun perhaps somewhat loosely; for example, the number 3.8 could occur more than once in such a "set".) The arithmetic mean is what pupils are taught very early to call the "average." If the set is a populasi statistik, then we speak of the population mean. If the set is a statistical sample, we call the resulting statistik a sample mean.

The mean may be conceived of as an estimate of the median. When the mean is not an accurate estimate of the median, the set of numbers, atawa sebaran frekuensi, is said to be skewed.

We denote the set of data by X = {x1, x2, ..., xn}. The symbol µ (Greek: mu) is used to denote the arithmetic mean of a population. We use the name of the variable, X, with a horizontal bar over it as the symbol ("X bar") for a sample mean. Both are computed in the same way:

$\overline{x}={\rm arithmetic\ mean}=(x_1+\cdots+x_n)/n.$

The arithmetic mean is greatly influenced by outliers. For instance, reporting the "average" annual income in Redmond, Washington as the arithmetic mean of all annual incomes would yield a surprisingly high number because of Bill Gates. These distortions occur when the mean is different from the median, and the median is a superior alternative when that happens.

In certain situations, the arithmetic mean is the wrong concept of "average" altogether. For example, if a stock rose 10% in the first year, 30% in the second year and fell 10% in the third year, then it would be incorrect to report its "average" increase per year over this three year period as the arithmetic mean (10% + 30% + (-10%))/3 = 10%; the correct average in this case is the geometric mean which yields an average increase per year of only 8.8%.

Lamun X nyaeta variabel acak, mangka nilai ekspektasi X bisa ditempo tina watesan-panjang mean aritmetik nyaeta kajadian unggal pengulangan pengukuran X. Ieu dipibanda ku hukum wilangan gede. Salaku hasil, sampel mean dipake keur estimasi nilai ekspektasi nu teu dipikanyaho.

Note that several other "means" have been defined, including the generalized mean, the generalized f-mean, the harmonic mean, the arithmetic-geometric mean, and the weighted mean.

## Lambang sejenna

Aritmetik mean kadangkala dilambangkeun make notasi jumlah, nyaeta:

$\overline{x} = \frac1n\sum_{i=1}^N x_i$

## Tempo ogé

(Waktu dipake salaku kata benda, kecap "arithmetic" is pronounced with the accent on the second syllable, but when used in the present sense, as an adjective, the accent is on the third syllable: "arithMETic")