Final answer:
The lower quartile of the given data set is 8.5 and the upper quartile is 25. Therefore, the correct answer is D) 8.5, 25.
Step-by-step explanation:
To find the lower quartile and upper quartile of the given data set, we first need to arrange the data in ascending order:
6, 6, 8, 9, 9, 10, 10, 18, 23, 23, 27, 30, 31
Next, we calculate the position of the lower quartile and upper quartile.
Lower Quartile:
The lower quartile represents the 25th percentile, which means that 25% of the data is below this value. To calculate the lower quartile, we take the median of the lower half of the data.
The lower half of the data is: 6, 6, 8, 9, 9, 10
The median of this lower half is the average of the two middle numbers: (8 + 9) / 2 = 8.5
Upper Quartile:
The upper quartile represents the 75th percentile, which means that 75% of the data is below this value. To calculate the upper quartile, we take the median of the upper half of the data.
The upper half of the data is: 18, 23, 23, 27, 30, 31
The median of this upper half is the average of the two middle numbers: (23 + 27) / 2 = 25
Therefore, the lower quartile is 8.5 and the upper quartile is 25. Hence the answer is D.