# QuartileDeviation

QuartileDeviation[list]

gives the quartile deviation or semi-interquartile range of the elements in list.

QuartileDeviation[dist]

gives the quartile deviation or semi-interquartile range of the distribution dist.

# Details # Examples

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## Basic Examples(2)

Quartile deviation for a list of exact numbers:

Quartile deviation of a parametric distribution:

## Scope(14)

### Data(11)

Exact input yields exact output:

Approximate input yields approximate output:

QuartileDeviation for a matrix gives columnwise ranges:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Compute results using other parametrizations:

Find the quartile deviation for WeightedData:

Find the quartile deviation for EventData:

Find the quartile deviation for TemporalData:

Find the quartile deviation for TimeSeries:

The quartile deviation depends only on the values:

Find the quartile deviation for data involving quantities:

### Distributions and Processes(3)

Find the quartile deviation for a parametric distribution:

Quartile deviation for a derived distribution:

Data distribution:

Quartile deviation for a time slice of a random process:

## Applications(4)

Obtain a robust estimate of dispersion when extreme values are present:

Measures based on the Mean are heavily influenced by extreme values:

Identify periods of high volatility in stock data using a five-year moving quartile deviation:

Compute QuartileDeviation for slices of a collection of paths of a random process:

Choose a few slice times:

Plot of the quartile deviations for the selected times:

Find the quartile deviation of the heights for the children in a class:

Plot the quartile deviation respective of the median:

## Properties & Relations(3)

QuartileDeviation is half the difference of linearly interpolated Quantile values:

InterquartileRange is twice QuartileDeviation:

QuartileDeviation is half the difference between the first and third quartiles:

## Possible Issues(1)

QuartileDeviation requires numeric values: ## Neat Examples(1)

The distribution of QuartileDeviation estimates for 20, 100 and 300 samples: