Question

question 16
complete the following statements.
a. the first quartile (q1) corresponds to the th percentile.
b. the median corresponds to the th percentile.
c. the third quartile (q3) corresponds to the th percentile.
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Explanation:

Step1: Recall quartile - percentile relationship

Quartiles divide a data set into four equal parts. The first quartile ($Q1$) is the value below which 25% of the data lies. By the definition of percentiles (a value below which a certain percentage of data lies), if 25% of the data is below $Q1$, then $Q1$ corresponds to the 25th percentile.

Step2: Recall median - percentile relationship

The median is the middle value of a data set. When the data is ordered, 50% of the data is below the median. Since a percentile $P_k$ is a value such that $k\%$ of the data is below it, the median corresponds to the 50th percentile.

Step3: Recall third - quartile percentile relationship

The third quartile ($Q3$) is the value below which 75% of the data lies. Using the percentile definition (a value below which a certain percentage of data lies), $Q3$ corresponds to the 75th percentile.

Answer:

a. 25
b. 50
c. 75