Which statement about quartiles is true?

• A. Q1 is the median of the entire dataset.
• B. Q3 is the median of the entire dataset.
• C. Q1 is the median of the lower half and Q3 is the median of the upper half.
• D. Quartiles are identical to the mean.

Answer: (C)

Quartiles split data that has been ordered into four equal parts. The first quartile, Q1, is found by taking the median of the lower half of the data, and the third quartile, Q3, is found by taking the median of the upper half. This means Q1 corresponds to the 25th percentile and Q3 to the 75th percentile.

For example, with data 1, 2, 3, 4, 5, 6, 7, 8, the lower half is 1, 2, 3, 4 and its median is (2 + 3) / 2 = 2.5, so Q1 = 2.5. The upper half is 5, 6, 7, 8 and its median is (6 + 7) / 2 = 6.5, so Q3 = 6.5. The overall median is 4.5, which lies between Q1 and Q3, not equal to either.

Quartiles describe positions in the data and are not the same as the mean, which is a single average value influenced by all data points. Therefore, the statement that Q1 is the median of the lower half and Q3 is the median of the upper half is the true one.