To find the median number of siblings from the given frequency table, we will follow these steps:
### Step 1: Expand the Frequency Table into a List
First, we need to create a list containing each number of siblings repeated according to its frequency.
From the table:
- 0 siblings: 9 times
- 1 sibling: 5 times
- 2 siblings: 7 times
- 3 siblings: 1 time
- 4 siblings: 3 times
Thus, the list will be:
[tex]\[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4\][/tex]
### Step 2: Sort the List
Next, we need to sort our list. In this case, expanding it according to frequencies already gives us a sorted list:
[tex]\[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4\][/tex]
### Step 3: Find the Median
The median is the middle value of the data set. If the number of data points, [tex]\(n\)[/tex], is odd, the median is the middle number in the list. If [tex]\(n\)[/tex] is even, the median is the average of the two middle numbers.
In our list, the total number of data points is:
[tex]\[9 + 5 + 7 + 1 + 3 = 25\][/tex]
Since 25 is an odd number, the median will be the [tex]\( \left(\frac{25 + 1}{2}\right) = \frac{26}{2} = 13 \)[/tex]-th element in the sorted list. Counting to the 13th element in the list:
[tex]\[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, \mathbf{1}, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4\][/tex]
The 13th element is 1.
### Conclusion
The median number of siblings is [tex]\(1\)[/tex].
