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
Leaves
1 14 4 5 5 6
2 2 3 3 5 5 6 6
124 8
01233 6 7
Key: 2 | 1 = 21
Stem
2
3
4
5
The quartiles divide the data into four equal parts.
1. First Quartile (Q1) represents the 25th percentile, or the value below which 25% of the data falls. In this case, Q1 is between the 6th and 7th values in the dataset.
6, 6, 7, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 20, 22, 23, 23, 24, 25, 25, 26, 26, 27, 30, 36, 37
Q1 = (13 + 13) / 2 = 13
2. Median (Q2) represents the 50th percentile, or the middle value of the dataset when listed in ascending order.
Q2 = 16
3. Third Quartile (Q3) represents the 75th percentile, or the value below which 75% of the data falls. In this case, Q3 is between the 20th and 21st values in the dataset.
20, 22, 23, 23, 24, 25, 25, 26, 26, 27, 30, 36, 37
Q3 = (25 + 26) / 2 = 25.5
Therefore, the quartiles for the commute times are as follows:
Q1 = 13 minutes
Q2 = 16 minutes
Q3 = 25.5 minutes