Quartiles
What Are Quartiles?
Quartiles are three specific values that divide a ranked data set into four equal parts, each representing 25% of the observations (Ken Black et al., 2018)(Prem S. Mann et al., 2016). As a special case of percentiles, the first quartile (Q1) corresponds to the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) represents the 75th percentile (Aliakbar Montazer Haghighi et al., 2020)(David Anderson et al., 2020). To determine these values accurately, the data must first be arranged in increasing order (Prem S. Mann et al., 2016)(Ned Freed et al., 2013).
Primary Components and Calculation
The calculation of quartiles involves finding the median of specific data subsets. Q1 is defined as the median of the observations lower than the overall median, while Q3 is the median of those greater than the median (Prem S. Mann et al., 2016)(M Van Rensburg et al., 2017). Together with the minimum and maximum values, quartiles form the "five-number summary," providing a snapshot of a distribution's characteristics (William Mendenhall et al., 2019). While various mathematical conventions exist for calculating these positions, they all aim to divide data into four equal groups (Ken Black et al., 2018)(David Anderson et al., 2020).
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Functional Application and Dispersion
Quartiles are essential for measuring data dispersion through the Interquartile Range (IQR), calculated as Q3 minus Q1 (Prem S. Mann et al., 2016)(Aliakbar Montazer Haghighi et al., 2020). The IQR represents the range of the "middle fifty" percent of the data points, offering a measure of variability less sensitive to extremes than the full range (Aliakbar Montazer Haghighi et al., 2020)(Roxy Peck et al., 2018). In practice, quartiles are used to construct box plots and identify outliers, which are often defined as values more than 1.5 times the IQR from the median (Andrew F. Hayes et al., 2020).