Answer:
Explanation:
To find the lower, middle, and higher quartiles of the given data set, we need to first order the data from lowest to highest:
5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19
The total number of values in the set is 12, so the middle value (or the median) will be the average of the 6th and 7th values:
Median = (9 + 10) / 2 = 9.5
To find the lower quartile (Q1), we take the median of the lower half of the data set, which includes the first six values:
Lower half: 5, 6, 7, 8, 9, 10
Q1 = median of the lower half = (7 + 8) / 2 = 7.5
To find the higher quartile (Q3), we take the median of the upper half of the data set, which includes the last six values:
Upper half: 12, 14, 15, 17, 18, 19
Q3 = median of the upper half = (15 + 17) / 2 = 16
Therefore, the lower quartile is 7.5, the middle quartile is 9.5, and the higher quartile is 16.