Question

complete the following statements.
a. in general, % of the values in a data set lie at or below the median.
b. % of the values in a data set lie at or below the first quartile (q1).
c. if a sample consists of 2100 test scores, of them would be at or below the second quartile (q2).
d. if a sample consists of 2100 test scores, of them would be at or above the third quartile (q3).

Explanation:

Step1: Recall the definition of median

The median divides a data set into two equal - parts. So, 50% of the values in a data set lie at or below the median.

Step2: Recall the definition of first quartile

The first quartile \(Q1\) is the value such that 25% of the data lies at or below it.

Step3: Recall the definition of second quartile

The second quartile \(Q2\) is the median. If there are \(n = 2100\) data points, the number of data points at or below \(Q2\) is \(0.5\times n\). Substitute \(n = 2100\), we get \(0.5\times2100=1050\).

Step4: Recall the definition of third quartile

The third quartile \(Q3\) is the value such that 75% of the data lies at or below it. So the number of data points at or above \(Q3\) is \((1 - 0.75)\times n\). Substitute \(n = 2100\), we get \(0.25\times2100 = 525\).

Answer:

a. 50
b. 25
c. 1050
d. 525