Questions: 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 2 1 1 4 4 5 5 6 3 2 2 3 3 5 5 6 6 4 1 2 4 8 5 0 1 2 3 3 6 7 Key: 2 1 = 21

Solution Steps

The commute times from the stem-and-leaf plot were extracted and converted into a sorted list of values:

\[ \text{Sorted Commute Times} = [21, 21, 24, 24, 25, 25, 26, 32, 32, 33, 33, 35, 35, 36, 36, 41, 42, 44, 48, 50, 51, 52, 53, 53, 56, 57] \]

To find the third quartile \( Q_3 \), we use the formula for the rank:

\[ \text{Rank} = Q \times (N + 1) = 0.75 \times (26 + 1) = 20.25 \]

Since the rank \( 20.25 \) is not an integer, we take the values at positions \( 20 \) and \( 21 \) in the sorted list:

\[ X_{\text{lower}} = 50 \quad \text{and} \quad X_{\text{upper}} = 51 \]

Using the averaging formula for the third quartile:

\[ Q_3 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{50 + 51}{2} = 50.5 \]

Final Answer