Answer :
First, we write the list of numbers in order:
[tex]$$10,\, 39,\, 71,\, 42,\, 39,\, 76,\, 38,\, 25.$$[/tex]
Step 1: Arrange the numbers in increasing order. The sorted list is:
[tex]$$10,\, 25,\, 38,\, 39,\, 39,\, 42,\, 71,\, 76.$$[/tex]
Step 2: Since there are [tex]$8$[/tex] numbers (an even number), the median is the average of the two middle numbers. The middle values are the [tex]$4^\text{th}$[/tex] and [tex]$5^\text{th}$[/tex] numbers in the sorted list.
Step 3: Identify the middle numbers. They are:
[tex]$$\text{Middle 1} = 39 \quad \text{and} \quad \text{Middle 2} = 39.$$[/tex]
Step 4: Calculate the median by averaging these two numbers:
[tex]$$\text{Median} = \frac{39 + 39}{2} = \frac{78}{2} = 39.$$[/tex]
Thus, the median is [tex]$\boxed{39}$[/tex].
[tex]$$10,\, 39,\, 71,\, 42,\, 39,\, 76,\, 38,\, 25.$$[/tex]
Step 1: Arrange the numbers in increasing order. The sorted list is:
[tex]$$10,\, 25,\, 38,\, 39,\, 39,\, 42,\, 71,\, 76.$$[/tex]
Step 2: Since there are [tex]$8$[/tex] numbers (an even number), the median is the average of the two middle numbers. The middle values are the [tex]$4^\text{th}$[/tex] and [tex]$5^\text{th}$[/tex] numbers in the sorted list.
Step 3: Identify the middle numbers. They are:
[tex]$$\text{Middle 1} = 39 \quad \text{and} \quad \text{Middle 2} = 39.$$[/tex]
Step 4: Calculate the median by averaging these two numbers:
[tex]$$\text{Median} = \frac{39 + 39}{2} = \frac{78}{2} = 39.$$[/tex]
Thus, the median is [tex]$\boxed{39}$[/tex].
