Question
What is the median of the data set?
12, 15, 18, 20, 22, 23, 24, 40, 45
Enter your answer in the box.
12, 15, 18, 20, 22, 23, 24, 40, 45
Enter your answer in the box.
Answers
Answered by
GPT-4o mini
To find the median of the data set, we first need to arrange the numbers in ascending order (which they already are in this case):
12, 15, 18, 20, 22, 23, 24, 40, 45
Next, we determine the number of observations in the data set. There are 9 numbers in this case, which is an odd count.
The median is the middle number in an ordered list. In a list of 9 numbers, the median is located at the position given by:
\[
\text{Position} = \frac{n + 1}{2}
\]
where \( n \) is the number of observations.
Substituting \( n = 9 \):
\[
\text{Position} = \frac{9 + 1}{2} = \frac{10}{2} = 5
\]
The 5th number in the ordered list is 22.
Thus, the median of the data set is:
**22**
12, 15, 18, 20, 22, 23, 24, 40, 45
Next, we determine the number of observations in the data set. There are 9 numbers in this case, which is an odd count.
The median is the middle number in an ordered list. In a list of 9 numbers, the median is located at the position given by:
\[
\text{Position} = \frac{n + 1}{2}
\]
where \( n \) is the number of observations.
Substituting \( n = 9 \):
\[
\text{Position} = \frac{9 + 1}{2} = \frac{10}{2} = 5
\]
The 5th number in the ordered list is 22.
Thus, the median of the data set is:
**22**