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 2 5 6 7
2 1 2 2 3 4 7
3 0 1 4 7 7 7 7 9
4 1 2 3 4 7 7 7 8
Key: 1|2=12
Step 1 of 3 : Find the second quartile.
The second quartile is the median of the data set, which is the middle value when the data is arranged in order.
Arranging the commute times in order from least to greatest:
12, 15, 16, 17, 21, 22, 22, 23, 24, 27, 30, 31, 34, 37, 37, 37, 37, 39, 41, 42, 43, 47, 47, 47, 48, 51
There are 26 data points in the set, so the middle value is between the 13th and 14th data points.
The 13th data point is 34 and the 14th data point is 37, so the second quartile (Q2 or the median) is 37 minutes.
Step 2 of 3: Find the first quartile.
The first quartile (Q1) is the median of the lower half of the data set.
Lower half of the data set: 12, 15, 16, 17, 21, 22, 22, 23, 24, 27, 30, 31, 34
There are 13 data points in the lower half of the set, so the middle value is between the 6th and 7th data points.
The 6th data point is 22 and the 7th data point is also 22, so the first quartile (Q1) is 22 minutes.
Step 3 of 3: Find the third quartile.
The third quartile (Q3) is the median of the upper half of the data set.
Upper half of the data set: 39, 41, 42, 43, 47, 47, 47, 48, 51
There are 13 data points in the upper half of the set, so the middle value is between the 6th and 7th data points.
The 6th data point is 47 and the 7th data point is also 47, so the third quartile (Q3) is 47 minutes.
Therefore, the quartiles for the commute times are:
Q1 = 22 minutes
Q2 = 37 minutes
Q3 = 47 minutes