5. the box plot represents the distribution of the number of children in 30 different families. after…

Explanation:

Step1: Recall median definition

The median is the middle - value when data is arranged in ascending or descending order. If there are $n$ data points, when $n$ is odd, the median is the $\left(\frac{n + 1}{2}\right)$-th value; when $n$ is even, the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th values.

Step2: Analyze effect of removing 12

Since 12 is the maximum value, it is either the largest value in the data - set or an outlier. Removing the maximum value does not affect the position of the middle - value(s) in the ordered data - set. For example, if we have an ordered data - set with $n$ values and $n$ is odd, say $n = 2k+1$ for some non - negative integer $k$. The median is the $(k + 1)$-th value. Removing the largest value (the $(2k + 1)$-th value) does not change the $(k + 1)$-th value. Similarly, for an even - numbered data - set with $n=2k$ values, the median is the average of the $k$-th and $(k + 1)$-th values, and removing the largest value (the $2k$-th value) does not change the $k$-th and $(k + 1)$-th values.

Answer:

The median is the middle value of the ordered data - set. The maximum value (12) is at the end of the ordered data - set. Removing it does not change the position of the middle value(s), so the median remains the same.