To determine the median number of siblings, let's go through the data step-by-step.
1. Organize Data in a List: First, we create a list where each number of siblings is listed multiple times, according to its frequency.
- 0 siblings occurs 4 times
- 1 sibling occurs 2 times
- 2 siblings occur 5 times
- 3 siblings occur 6 times
- 4 siblings occur 8 times
Thus, the data set is:
[tex]\[
[0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4]
\][/tex]
2. Sort the List: This is already sorted in the step before:
[tex]\[
[0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4]
\][/tex]
3. Calculate the Number of Data Points: Count the total number of siblings reported:
[tex]\[
4 + 2 + 5 + 6 + 8 = 25
\][/tex]
There are 25 data points in total.
4. Determine the Median:
- Median is the middle value in the ordered list.
- Since we have 25 data points (which is an odd number), the median is the value at the position [tex]\( \left(\frac{25 + 1}{2}\right) \)[/tex], i.e., the 13th position in the sorted list.
5. Find the Median in the Sorted List:
- The 13th value in our sorted list is:
[tex]\[
[0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, \mathbf{3}, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4]
\][/tex]
Counting the positions:
- 12th position is the first 3
- 13th position is another 3
Therefore, the median number of siblings is [tex]\(\boxed{3}\)[/tex].
