Question

caroline asks 12 gym - members how many months they have each been a member at the gym. the 12 responses are listed: 1,2,2,4,5,5,7,7,9,11,11,14. caroline wants to make a box - plot for her data. she determines four of the five statistical measurements needed to make a box - plot and plots these four measurements on a number line as shown. number line with points marked at 1, 4, 9, 14 and label months of membership at gym. what is the value of the remaining statistical measurement caroline needs so she can make a box - plot for her data?

Explanation:

Step1: Recall box - plot measurements

A box - plot requires five - number summary: minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum.

Step2: Identify given data

The data set is \(1,2,2,4,5,5,7,7,9,11,11,14\). Assume the four given points on the number line are minimum, \(Q_1\), \(Q_3\), and maximum. We need to find the median.

Step3: Calculate the median

Since there are \(n = 12\) data points, the median is the average of the \(\frac{n}{2}=6\)th and \((\frac{n}{2}+1)=7\)th ordered data points. The 6th value is 5 and the 7th value is 7. The median is \(\frac{5 + 7}{2}=6\).

Answer:

6