Find \( Q_{1}, Q_{3} \), and IQR. (Round your answers to one decimal place as needed.) \[ Q_{1}=\square \] \( Q_{3}=\square \) List any outliers. Use the "Does not exist" button if there are none. \( \square \)
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Bonus Knowledge
To find \( Q_{1} \), \( Q_{3} \), and the Interquartile Range (IQR), you first need to arrange your data in ascending order. Once sorted, \( Q_{1} \) is the median of the lower half of the dataset, and \( Q_{3} \) is the median of the upper half. The IQR is computed as \( IQR = Q_{3} - Q_{1} \). Suppose your sorted dataset is: 2, 3, 5, 6, 7, 8, 12, 13, 14. 1. **Find \( Q_{1} \)**: The lower half is 2, 3, 5, 6. The median of this set is 4. 2. **Find \( Q_{3} \)**: The upper half is 8, 12, 13, 14. The median of this set is 12.5. 3. **Calculate IQR**: \( IQR = Q_{3} - Q_{1} = 12.5 - 4 = 8.5 \). Outliers can typically be determined by calculating \( 1.5 \times IQR \). Any value below \( Q_{1} - 1.5 \times IQR \) or above \( Q_{3} + 1.5 \times IQR \) may be considered an outlier. If any values in your dataset fall outside this range, those are your outliers. Otherwise, select "Does not exist."