Sure, let's determine how much the median of the list increases when we add the number 14 to the existing list.
### Step 1: Find the original median
First, we need to determine the median of the original list:
[tex]$
[8, \quad 15, \quad 20, \quad 10, \quad 3]
$[/tex]
We start by sorting the list in ascending order:
[tex]$
[3, \quad 8, \quad 10, \quad 15, \quad 20]
$[/tex]
Since the list has an odd number of elements (5), the median is the middle element:
[tex]$
\text{Original median} = 10
$[/tex]
### Step 2: Add the new value and find the new median
Next, we add the number 14 to the list, making it:
[tex]$
[8, \quad 15, \quad 20, \quad 10, \quad 3, \quad 14]
$[/tex]
Sort this new list:
[tex]$
[3, \quad 8, \quad 10, \quad 14, \quad 15, \quad 20]
$[/tex]
Since the new list has an even number of elements (6), the median is the average of the two middle numbers. The two middle numbers in the sorted list are 10 and 14:
[tex]$
\text{New median} = \frac{10 + 14}{2} = 12
$[/tex]
### Step 3: Calculate the increase in the median
Finally, we calculate the increase in the median:
[tex]$
\text{Increase in median} = \text{New median} - \text{Original median} = 12 - 10 = 2
$[/tex]
### Conclusion
So, the median increases by 2 when we add the number 14 to the original list.
