## Key Concepts About Means

Means are measures of a central tendency. In this section, you will learn
about three types of means:

- arithmetic,
- weighted arithmetic, and
- geometric.

### Arithmetic Means

The finite population mean of X_{1} , X_{2} ,…. X_{N}
is defined as the sum of the values X_{i} divided by the population size
N. Typically, in a non-survey setting an arithmetic mean is estimated by taking a simple random
sample of the finite population, x_{1}, x_{2},…,x_{n, }
summing the values and dividing by the sample size n.

#### Equation for Arithmetic Mean

This is often referred to as the arithmetic mean. On average, the result of
the arithmetic mean would be expected to equal the result of the population
mean.

### Weighted arithmetic means

For NHANES 1999-2002 a sample weight, w_{i}, is
associated with each sample person. The sample weight is a
measure of the number of people in the population represented by
that person. For more information on sample weights, please see
the Weighting module. To obtain an unbiased estimate of the
population mean, based on data from the NHANES 1999-2002 sample,
it is necessary to take a **weighted **arithmetic mean.

#### Equation for Weighted Arithmetic Mean

### Geometric Means

In instances where the data are highly skewed, geometric means can be
used. A geometric mean, unlike an arithmetic mean, minimizes the effect of very
high or low values, which could bias the mean if a straight average (arithmetic
mean) were calculated. The geometric mean is a log-transformation of the data
and is expressed as the N-th root of the product of N numbers.

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