To find the value of [tex]\( x \)[/tex] in the data set [tex]\( 9, 10, 12, x, 20, 25 \)[/tex] such that the median is 14, follow these steps:
1. Organize the Given Data: We first recognize the data set we are given:
[tex]\[
9, 10, 12, x, 20, 25
\][/tex]
2. Understand the Median: The median of a set of numbers is the middle value of the set when the numbers are listed in order. If the set has an odd number of elements, the median is the middle number. If the set has an even number of elements, the median is the average of the two middle numbers.
In this problem, the median is given as 14, and the data set has an even number of elements (6 elements).
3. Determine the Placement of [tex]\( x \)[/tex]: For the median to be 14, the middle values when the list is sorted must average to 14. Since our set has 6 elements, those values must be the 3rd and 4th elements in the sorted list.
4. Incorporate the Median: We need to place 14 correctly within the data set so that it becomes one of the middle values when the list is sorted.
- When we insert 14 into the list and sort it, we get:
[tex]\[
9, 10, 12, 14, 20, 25
\][/tex]
5. Identify [tex]\( x \)[/tex]: From the sorting step, it is clear that the value [tex]\( x \)[/tex] must be 14 in order to make the list sorted properly and ensure the median value of 14.
Thus, the value of [tex]\( x \)[/tex] must be:
[tex]\[
x = 14
\][/tex]
