Arithmetic mean

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

The méan may be conceived of as an estimate of the median. When the méan 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, ..., x_n}. The symbol µ (Greek: mu) is used to denote the arithmetic méan 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 méan. Both are computed in the same way:

${\overline {x}}={\rm {arithmetic\ mean}}=(x_{1}+\cdots +x_{n})/n.$

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

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

Lamun X nyaéta variabel acak, mangka nilai ekspektasi X bisa ditempo tina watesan-panjang méan aritmetik nyaéta kajadian unggal pengulangan pengukuran X. Ieu dipibanda ku hukum wilangan gedé. Salaku hasil, sampel méan dipaké 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 méan kadangkala dilambangkeun maké notasi jumlah, nyaéta:

${\overline {x}}={\frac {1}{n}}\sum _{i=1}^{N}x_{i}$

Tempo ogé

mean, average, kasimpulan statistik, varian, central tendency, simpangan baku, inequality of arithmetic and geometric means

(Waktu dipaké 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")

Tumbu kaluar

• Arithmetic and geometric means