Question

determine whether the following statement is true or false.
a score in the 50th percentile on a standardized test is the median.
choose the correct answer below.
○ a. the statement is false because the median, or first quartile, is the 25th percentile
○ b. the statement is false because a score in the 50th percentile is the standard deviation
○ c. the statement is true because the median, or second quartile, is the 50th percentile
○ d. the statement is false because the median, or third quartile, is the 75th percentile

Explanation:

Step1: Recall the definition of percentile and median

The \(n\)th percentile of a data set is a value such that \(n\%\) of the data values are less than or equal to this value. The median of a data set divides the data into two equal - sized parts. That is, \(50\%\) of the data values are less than or equal to the median and \(50\%\) of the data values are greater than or equal to the median.
The first quartile \(Q_1\) is the \(25\)th percentile ( \(25\%\) of the data is less than or equal to \(Q_1\) ), the second quartile \(Q_2\) (which is the median) is the \(50\)th percentile ( \(50\%\) of the data is less than or equal to \(Q_2\) ), and the third quartile \(Q_3\) is the \(75\)th percentile ( \(75\%\) of the data is less than or equal to \(Q_3\) ).

Step2: Analyze each option

• Option A: The first quartile \(Q_1\) is the \(25\)th percentile, not the median. The median is the \(50\)th percentile. So, this option is incorrect.
• Option B: The standard deviation is a measure of the spread of the data, not related to the percentile in this context. So, this option is incorrect.
• Option C: Since the median (second quartile \(Q_2\)) has the property that \(50\%\) of the data is less than or equal to it, the median is the \(50\)th percentile. This option is correct.
• Option D: The third quartile \(Q_3\) is the \(75\)th percentile, not the median. The median is the \(50\)th percentile. So, this option is incorrect.

Answer:

C. The statement is true because the median, or second quartile, is the 50th percentile.