\[ 10,18,4,15,3,21, x \] If \( x \) is the median of the 7 numbers listed above, which of the following could be the value of \( x \) ?

To find the median of the seven numbers \( 10, 18, 4, 15, 3, 21, x \), we first need to arrange the numbers in increasing order. The median is the middle value, which means it will be the fourth number in this ordered list since there are seven numbers total. 1. Sorting the existing numbers: \( 3, 4, 10, 15, 18, 21 \) 2. We know that \( x \) will insert into this list and affect the median. The median will depend on the value of \( x \): - If \( x \leq 3 \), the sorted list becomes \( x, 3, 4, 10, 15, 18, 21 \) with the median being \( 10 \). - If \( 3 < x \leq 4 \), the list will be \( 3, x, 4, 10, 15, 18, 21 \), median remains \( 10 \). - If \( 4 < x < 10 \), the list will be \( 3, 4, x, 10, 15, 18, 21 \) with median as \( 10 \). - If \( x = 10 \), the list is \( 3, 4, 10, 10, 15, 18, 21 \) giving a median of \( 10 \). - If \( 10 < x < 15 \), it looks like \( 3, 4, 10, x, 15, 18, 21 \), keeping the median at \( 10 \). - If \( x = 15 \), it becomes \( 3, 4, 10, 15, 15, 18, 21 \) with the median still \( 15 \). - If \( 15 < x < 18 \), it becomes \( 3, 4, 10, 15, x, 18, 21 \), making the median \( 15 \). - If \( x = 18 \), it becomes \( 3, 4, 10, 15, 18, 18, 21 \) with a median of \( 15 \). - If \( 18 < x < 21 \), then \( 3, 4, 10, 15, 18, x, 21 \) keeps the median at \( 15 \). - If \( x \geq 21 \), the list will be \( 3, 4, 10, 15, 18, 21, x \) making the median \( 15 \). The possible values of \( x \) that could serve as the median are: - \( 10 \) - \( 15 \) Thus, the values \( x \) could take to meet the median requirement are \( 10 \) or any value between \( 10 \) and \( 15 \).