29. Which of the following numbers represents the median of the following data set? 23, 19, 22, 17, 20, 18, 22
Answer: A
The median of the data set is 20.
To find the median, the data set must first be arranged in ascending order, resulting in: 17, 18, 19, 20, 22, 22, 23. The median is the middle number, which in this case is 20, as it is the fourth number in the ordered set.
A) 20
This option correctly identifies the median of the data set. After arranging the numbers in ascending order, the fourth value (20) is indeed the middle number of the seven total values, validating that 20 is the median.
B) 17
This option is incorrect as 17 is the smallest number in the ordered set and does not represent the middle value. The median cannot be the lowest number when the data set has other values above it.
C) 21
This option is also incorrect since 21 is not present in the data set. The median must be an actual number from the data set, and 21 does not fit that criterion.
D) 22
While 22 is one of the numbers in the data set, it does not represent the median. In the ordered list, 22 is the fifth and sixth number, thus not the middle value when considering the total count of seven numbers.
Conclusion
The correct median of the data set is 20, as it is the middle value when the numbers are organized in ascending order. All other options either misidentify the median or do not exist within the provided data, making them incorrect.