Answer :
To solve the problem, we are given a list of numbers: [tex]\(5, 7, 8, 11, x+1, 15, 19, 21\)[/tex], and 25. The numbers are in ascending order, and we are told that the median of these numbers is 15. We need to find the value of [tex]\(x\)[/tex].
Here’s the step-by-step approach:
1. Count the Total Numbers: First, observe that there are a total of 9 numbers in this list.
2. Identify the Median Position: The median is the middle number in an ordered list. Since there are 9 numbers, the median will be at the 5th position when they are in ascending order (since [tex]\((9 + 1) / 2 = 5\)[/tex]).
3. Assign the Median: We know the median is 15. According to the problem, this means the middle number, which is the 5th number in the list, should be 15.
4. Find the 5th Number: Looking at our list:
- The first four numbers are given as 5, 7, 8, 11.
- The 5th number is [tex]\(x + 1\)[/tex].
Since the median (the 5th number) is 15, we have:
[tex]\[
x + 1 = 15
\][/tex]
5. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], simply solve the equation:
[tex]\[
x + 1 = 15
\][/tex]
Subtract 1 from both sides:
[tex]\[
x = 15 - 1 = 14
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is 14.
Here’s the step-by-step approach:
1. Count the Total Numbers: First, observe that there are a total of 9 numbers in this list.
2. Identify the Median Position: The median is the middle number in an ordered list. Since there are 9 numbers, the median will be at the 5th position when they are in ascending order (since [tex]\((9 + 1) / 2 = 5\)[/tex]).
3. Assign the Median: We know the median is 15. According to the problem, this means the middle number, which is the 5th number in the list, should be 15.
4. Find the 5th Number: Looking at our list:
- The first four numbers are given as 5, 7, 8, 11.
- The 5th number is [tex]\(x + 1\)[/tex].
Since the median (the 5th number) is 15, we have:
[tex]\[
x + 1 = 15
\][/tex]
5. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], simply solve the equation:
[tex]\[
x + 1 = 15
\][/tex]
Subtract 1 from both sides:
[tex]\[
x = 15 - 1 = 14
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is 14.
