The secondary quartile is equal to:

Question

Accepted Answer

The correct option is 1:
In descriptive statistics, quartiles are values that divide a data set into four equal parts, each containing 25% of the data points. There are three main quartiles: the first quartile ($Q\_1$), the second quartile ($Q\_2$), and the third quartile ($Q\_3$). The secondary quartile, often denoted as $Q\_2$, is the point in the distribution that marks the 50% mark of the data when it is ordered. By definition, the Median is also the central value of an ordered data set, dividing the data into two equal halves. Since the secondary quartile ($Q\_2$) lies exactly in the middle of the data set, it is precisely equal to the Median. Both measures represent the point below which 50% of the observations fall, making them identical conceptually and mathematically.

The incorrect option is 2 (3rd Percentile): The 3rd Percentile is the value below which only 3% of the data falls. The secondary quartile, $Q_2$, represents the 50th percentile, making the 3rd percentile far too low to be equal to $Q_2$.

The incorrect option is 3 (4th Percentile): Similarly, the 4th Percentile represents the value below which 4% of the data lies. Since the secondary quartile must represent the 50% mark, the 4th percentile is an incorrect measure for $Q_2$.

The incorrect option is 4 (Quartile deviation): Quartile deviation, also known as the Semi-Interquartile Range, is a measure of dispersion or variability. It is calculated as half the difference between the third and first quartiles ($\frac{Q_3 - Q_1}{2}$). Quartile deviation is a range and not a positional measure of central tendency like the secondary quartile.