The data is divided into four equal parts by quartiles. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) represents the 75th percentile. These quartiles help to understand the distribution of the data by segmenting it into four intervals, each containing approximately 25% of the observations.
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They are called the quartiles. The middle one is also known as the median.
Four equal parts equals both fourths and quarters.
"Trisecting" is cutting into three equal parts, not four. Trisecting is impossible. Cutting into four equal parts is possible though, and trivial once you know how to bisect an angle.
quarter
Yes. For example, 4/7 represents four out of seven equal parts of something.