Questions: Homework 9 - 3.3 Question 2 of 5 (1 point) I Question Attempt: 1 of Unlimited For the data set 3 6 5 12 3 7 5 14 3 7 5 23 4 10 5 28 5 10 6 6 5 12 Part 1 of 4 (a) Find the first and third quartiles. The first quartile is The third quartile is.

Solution Steps

The given data set is sorted as follows: \[ \text{Sorted Data} = [3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 10, 10, 12, 12, 14, 23, 28] \]

To find the first quartile \(Q_1\), we use the formula: \[ \text{Rank} = Q \times (N + 1) = 0.25 \times (22 + 1) = 5.75 \] This indicates that \(Q_1\) lies between the 5th and 6th values in the sorted data. The values are both 5, so we calculate: \[ Q_1 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{5 + 5}{2} = 5.0 \]

To find the third quartile \(Q_3\), we use the formula: \[ \text{Rank} = Q \times (N + 1) = 0.75 \times (22 + 1) = 17.25 \] This indicates that \(Q_3\) lies between the 17th and 18th values in the sorted data. The values are 10 and 12, so we calculate: \[ Q_3 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{10 + 12}{2} = 11.0 \]

Final Answer