Final answer:
The third quartile (Q3) is the median of the upper half of the data set excluding the overall median. Since the data set is 12, 16, 19, 20, 26, 34, 43, 47, 49 and the median is 26, we exclude it to find the median of 34, 43, 47, 49, resulting in Q3 being 43.
Step-by-step explanation:
To find the third quartile (Q3) of the data set (12, 16, 19, 20, 26, 34, 43, 47, 49), you should first determine that Q3 is the median of the upper half of the data set, not including the median of the entire data set if there is an odd number of values. Since the data set provided has an odd number of values (nine), you remove the median value of the entire data set and calculate the median of the remaining upper half.
Let's start by finding the median of the entire data set, which is the middle value when the numbers are sorted in ascending order. The data set has nine values, so the median is the fifth number: 26. We then split the data set into two halves, excluding 26:
- Lower half: 12, 16, 19, 20
- Upper half: 34, 43, 47, 49
The third quartile (Q3) is the median of the upper half. Since there are four numbers in the upper half, the median is the average of the two middle numbers, which are 43 and 47. Therefore, Q3 is (43 + 47) / 2 = 45. However, since our options only contain whole numbers, we must choose the number that is closest to our calculated Q3 without going over, which is 43 from the provided options. The answer is option c. 43.