Questions: Module 3 ALEKS Practice Homework Question 19 of 33 (4 points) Question Attempt: 1 of 3 For the data set 14 40 19 44 37 84 6 24 69 38 29 Part 1 of 4 (a) Find the first and third quartiles. The first quartile is 19. The third quartile is 44. Part 2 of 4 (b) Find the IQR. IQR=25 Part 3 of 4 (c) Find the upper and lower outlier boundaries. The lower outlier boundary is . The upper outlier boundary is .

Solution Steps

The given data set is: \[ \{14, 40, 19, 44, 37, 84, 6, 24, 69, 38, 29\} \] After sorting, the data becomes: \[ \{6, 14, 19, 24, 29, 37, 38, 40, 44, 69, 84\} \]

To find the first quartile \(Q_1\), we use the formula: \[ \text{Rank} = Q \times (N + 1) = 0.25 \times (11 + 1) = 3.0 \] The quantile is at position 3, which corresponds to the value: \[ Q_1 = 19 \]

To find the third quartile \(Q_3\), we use the formula: \[ \text{Rank} = Q \times (N + 1) = 0.75 \times (11 + 1) = 9.0 \] The quantile is at position 9, which corresponds to the value: \[ Q_3 = 44 \]

The interquartile range (IQR) is calculated as: \[ IQR = Q_3 - Q_1 = 44 - 19 = 25 \]

The lower outlier boundary is calculated as: \[ \text{Lower Outlier Boundary} = Q_1 - 1.5 \times IQR = 19 - 1.5 \times 25 = -18.5 \] The upper outlier boundary is calculated as: \[ \text{Upper Outlier Boundary} = Q_3 + 1.5 \times IQR = 44 + 1.5 \times 25 = 81.5 \]

Final Answer