Understanding Interquartile Range and Quartile Deviation
The interquartile range (IQR) and quartile deviation (QD) are both measures of statistical dispersion. Although related, they serve different purposes in data analysis.

Interquartile Range (IQR)
- The IQR is the difference between the third quartile (Q3) and the first quartile (Q1):
IQR = Q3 - Q1
- It represents the range within which the central 50% of the data lies.
- The IQR is particularly useful for identifying outliers, as it focuses on the middle portion of the dataset and ignores extreme values.

Quartile Deviation (QD)
- The quartile deviation, also known as the semi-interquartile range, is half of the IQR:
QD = (Q3 - Q1) / 2
- It provides a measure of the spread of the middle 50% of the data, offering insights into the variability within that range.
- The QD is useful for comparing the dispersion of different datasets, particularly when they have similar central tendencies.

Relationship Between IQR and QD
- The IQR is thus **twice** the quartile deviation:
IQR = 2 × QD
- This relationship highlights that while both metrics convey similar information about data spread, the IQR gives a full range, while the QD provides a more compact measure.
In summary, the interquartile range is a more extensive measure of dispersion, while the quartile deviation offers a concise view of variability within the central portion of the data. Understanding both helps in a comprehensive analysis of statistical data.