Calculating Quartiles from Data Set
In the image, you are given a set of data and asked to find the lower quartile, median, and upper quartile.
To find these measures, you first need to make sure the data is sorted in ascending order, which it is. The dataset contains the following numbers:
13, 17, 20, 26, 37, 39, 40, 82, 85, 88, 88
To find the median (the middle value), since there are 11 data points, you take the middle value, which is the 6th number when the data is ordered. The 6th number in the sequence is 39, so the median is 39.
The lower quartile (Q1) is the median of the first half of the data. Since there are 11 data points, we take the lower 5 data points (ignoring the median):
13, 17, 20, 26, 37
The middle of this set is the third value, which is 20, so the lower quartile is 20.
The upper quartile (Q3) is the median of the second half of the data. Again, we ignore the median (39) and take the upper 5 data points:
40, 82, 85, 88, 88
The middle of this set is the third value, which is 85, so the upper quartile is 85.
To summarize:
Lower quartile (Q1) = 20
Median = 39
Upper quartile (Q3) = 85
