The following stem-and-leaf plot represents the times in minutes required for 26
co-workers to commute to work. Use the data provided to find the quartiles.
Commute Times in Minutes
Stem Leaves
1
0
4
4
6
6
6
9
2
2
4
4
5
8
3
3
4
4
5
6
8
4
0
0
3
3
5
6
7
8
Key: 1|0=10
Step 1 of 3 : Find the second quartile.
The second quartile is the median of the data set, which divides the data into two halves.
First, let's organize the data in ascending order:
0, 0, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 10, 20, 22, 24, 34, 44, 46, 68
There are 26 data points, so the median is the average of the 13th and 14th data points:
Median = (6 + 6) / 2 = 6
Therefore, the second quartile (Q2) is 6.
Step 2 of 3: Find the first quartile.
The first quartile (Q1) is the median of the lower half of the data set.
The lower half of the data set is: 0, 0, 3, 3, 4, 4, 4, 4, 5, 5
There are 10 data points in the lower half, so the median of the lower half is the average of the 5th and 6th data points:
Median = (4 + 4) / 2 = 4
Therefore, the first quartile (Q1) is 4.
Step 3 of 3: Find the third quartile.
The third quartile (Q3) is the median of the upper half of the data set.
The upper half of the data set is: 6, 6, 6, 6, 7, 8, 8, 8, 10, 20, 22, 24, 34, 44, 46, 68
There are 16 data points in the upper half, so the median of the upper half is the average of the 8th and 9th data points:
Median = (8 + 8) / 2 = 8
Therefore, the third quartile (Q3) is 8.
In summary, the quartiles for the commute times in minutes data set are:
Q1 = 4
Q2 = 6
Q3 = 8