Question

the six - by - six grid contains the ages of actors in a youth shakespeare festival. 8 cells were randomly selected using number cubes. the results are shown below. calculate the median of the values. 13, 13, 14, 11, 10, 15, 13, 14 the median of the values is \boxed{}

Explanation:

Step1: Order the data set

First, we need to order the given data set: \(8, 9, 9, 10, 10, 10, 11, 13, 13, 13, 14, 14, 14, 15, 15, 15\)? Wait, no, wait the data from the 8 cells: Wait, the problem says 8 cells were randomly selected. Wait, the list given is: 13,13,14,11,10,15,13,14? Wait, no, the user's text: "13,13,14,11,10,15,13,14" – wait, let's check the numbers. Wait, the grid is six-by-six, but 8 cells selected: Wait, the numbers provided in the problem (the 8 values? Wait, the text says: "13,13,14,11,10,15,13,14" – wait, let's count: 13,13,14,11,10,15,13,14. Wait, that's 8 numbers? Wait, no, the user's text: "13,13,14,11,10,15,13,14" – let's list them: 10, 11, 13, 13, 13, 14, 14, 15. Wait, no, let's sort them properly. Wait, the numbers are: 13,13,14,11,10,15,13,14. Let's sort them in ascending order: 10, 11, 13, 13, 13, 14, 14, 15. Now, to find the median of 8 numbers (even count), the median is the average of the 4th and 5th terms.

Step1: Sort the data

First, sort the data set: \(10, 11, 13, 13, 13, 14, 14, 15\)

Step2: Find the middle terms

Since there are 8 values (even number of observations), the median is the average of the \(\frac{8}{2} = 4\)th and \((\frac{8}{2} + 1) = 5\)th terms.

The 4th term is \(13\) and the 5th term is \(13\).

Step3: Calculate the median

Median = \(\frac{13 + 13}{2} = \frac{26}{2} = 13\)

Answer:

13