Use this data set for all problems in this practice: 15, 12, 11, 16, 17, 12, 11, 17, 12
What are the lower quartile and upper quartile?
To find the lower and upper quartiles, first arrange the data set in ascending order:
11, 11, 12, 12, 12, 15, 16, 17, 17
The lower quartile is the value that separates the lowest 25% of the data set from the higher 75% of the data set. In this case, the lower quartile is the 25th percentile, which is the value at the index:
(9 + 1) * 0.25 = 2.5
Since the index is not a whole number, we take the average of the 2nd and 3rd values, which are both 11. Thus, the lower quartile is 11.
The upper quartile is the value that separates the highest 25% of the data set from the lower 75% of the data set. In this case, the upper quartile is the 75th percentile, which is the value at the index:
(9 + 1) * 0.75 = 7.5
Again, since the index is not a whole number, we take the average of the 7th and 8th values, which are both 17. Thus, the upper quartile is 17.
Therefore, the lower quartile is 11 and the upper quartile is 17.