To determine the median number of siblings from the given survey data, let's follow these steps:
1. Create a List of All Data Points:
First, we need to list out each data point according to its frequency. Here’s the given table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of siblings} & \text{Frequency} \\
\hline
0 & 9 \\
\hline
1 & 5 \\
\hline
2 & 7 \\
\hline
3 & 1 \\
\hline
4 & 3 \\
\hline
\end{array}
\][/tex]
Based on this table, we create a list with the number of siblings appearing according to their frequencies:
[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]
2. Order the List:
The list is already ordered, but to ensure clarity, here it is again:
[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]
3. Find the Median:
To find the median, we need to determine the middle value in this list. If the number of observations (n) is odd, the median is the middle number. If n is even, the median is the average of the two middle numbers.
- Count the total number of data points: [tex]\( n = 25 \)[/tex].
Since [tex]\( n = 25 \)[/tex], an odd number, the median is the middle value. The middle value is located at position:
[tex]\[
\frac{n + 1}{2} = \frac{25 + 1}{2} = 13
\][/tex]
So, the 13th value in the ordered list is the median. If we count the values:
[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 value is 1.
Therefore, the median number of siblings is 1.
