15, 12, 11, 16, 17, 12, 11, 17, 12
What are the lower quartile and upper quartile?
To find the lower quartile and upper quartile, first we need to arrange the given numbers in increasing order:
11, 11, 12, 12, 12, 15, 16, 17, 17
The lower quartile (Q1) is the median of the lower half of the data set. In this case, the lower half of the numbers is 11, 11, 12, and 12. The median of this subset is equal to the average of the two middle numbers, which is (11+12)/2 = 23/2 = 11.5.
The upper quartile (Q3) is the median of the upper half of the data set. In this case, the upper half of the numbers is 15, 16, 17, and 17. The median of this subset is equal to the average of the two middle numbers, which is (16+17)/2 = 33/2 = 16.5.
Therefore, the lower quartile (Q1) is 11.5 and the upper quartile (Q3) is 16.5.