Types of averages

Here is a list of the types of averages used in statistics also called measures of central tendency. We start with the common type.

The most common types of averages are the mean, median, and mode.

Mean

The mean is found by adding all the numbers in a list and then divide by how many numbers there are.

Let x1, x2, ... , xn be a list.

  Mean =
x1 + x2 +...+ xn / n

Median

The median is the middle value when a list of numbers is ordered from least to greatest or from greatest to least.

Mode 

The mode is(are) the number(s) which occur(s) most often.

Harmonic mean

The harmonic mean is found by dividing the numbers of values by the sum of the reciprocals of all values.

Let n be the number of values or how many numbers there are


$$ Harmonic \ mean = \frac{n}{\Sigma \frac {1}{x} } $$


Notice that x represents a set of numbers such as {x1, x2, ... , xn}

Quadratic mean

The quadratic mean is found by squaring each value, adding the results, dividing by the numbers of values, and then taking the square root of that result.

$$ Quadratic \ mean = \sqrt{\frac{\Sigma x^{2}}{n}} $$

Notice again that x represents a set of numbers such as {x1, x2, ... , xn}

Geometric mean

Given n values that are positive, the geometric mean is the nth root of their product.

$$ Geometric \ mean = \sqrt[{n}]{x_1\times x_2 \ ... \ \times \ x_n} $$

Weighted mean

The weighted mean is found by adding the product of each weight and each value and then dividing by the sum of all weight.

Let w represents each weight and let x represent each value.

  Weighted mean =
Σw × x / Σw

Trimmed mean or truncated mean

Let x be a number 

After putting a data set in order, the x% trimmed mean is found deleting the bottom x% of the values and the top x% of the values and calculating the mean of the remaining values.

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