Quartile Ranges
Explanation
There are some measures of dispersion that instead of using the full range (i.e. maximum minus minimum), make use of the quartiles. The advantage of this, is that it is less influenced by extreme values.
The Interquartile Range (Galton, 1881, p. 245) is the range how big the difference is between the third and the first quartile. If Tukey's method for the quartiles is used, referred to as hinges, this is then also known as H-spread (Tukey, 1977, p. 44)
Yule (1911, p. 147) used half the inter-quartile range and labelled this Semi-Interquartile Range which he preferred over the term Quartile Deviation
There is also a measure of central tendency that uses the quartiles, the Mid-Quartile (Parzen, 1980, p. 19), which is the average of the first and second quartile. It is also sometimes referred to as the Mid-Quartile Range (see for example Luo et al. (2018, p. 2), who refer to Triola, but Triola doesn't add the 'range' (Triola, 2010, p. 120))
Obtaining the Measure
with Excel
Excel file from videos: ME - Quartile Ranges (E).xlsm
using stikpetE
without using stikpetE
with Python
Notebook from video: ME - Quartile Ranges (P).ipynb
using stikpetP
without using stikpetP
with SPSS
Formula
Using \(Q_1\) to indicate the value of the first quartile, and \(Q_3\) for the third quartile, we can have the following formulas.
The Interquartile Range (IQR) (Galton, 1881, p. 245):
\(IQR = Q_3 - Q_1\)
The Semi-Interquartile Range (SIQR) or Quartile Deviation (Yule, 1911, p. 147):
\(SIQR = \frac{Q_3 - Q_1}{2}\)
The Mid-Quartile or Mid-Quartile Range (MQR) (Parzen, 1980, p. 19):
\(MQR = \frac{Q_3 + Q_1}{2}\)
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