The prices of 14 different randomly selected \( 35-\mathrm{mm} \) compact cameras are as follows: \( \$ 169, \$ 225, \$ 129, \$ 175, \$ 299, \$ 140, \$ 215, \$ 239, \$ 1, \$ 99, \$ 149, \$ 219 \), \( \$ 120 \), and \( \$ 144 \). Use the interquartile range approach \( \left(Q_{1}-1.5 \times\right. \) IQR, \( Q_{3}+1.5 \times \) IQR) to find whether any of the amounts are outliers. List any outliers. Select all that apply. 239 none of these 90 1

To determine if there are any outliers in the given prices of the cameras using the interquartile range (IQR) method, we first need to calculate the first quartile \( Q_1 \), the third quartile \( Q_3 \), and the IQR itself. ### Step 1: Sort the Data First, let's sort the prices in ascending order: \[ 1, 99, 120, 129, 140, 144, 149, 169, 175, 215, 219, 225, 239, 299 \] ### Step 2: Calculate \( Q_1 \) and \( Q_3 \) - **Finding \( Q_1 \)**: This is the median of the first half of the data. - The first half (lower half) is: \( 1, 99, 120, 129, 140, 144, 149 \) - The median of this half (7 values) is the 4th value: \( Q_1 = 129 \) - **Finding \( Q_3 \)**: This is the median of the second half of the data. - The second half (upper half) is: \( 169, 175, 215, 219, 225, 239, 299 \) - The median of this half (7 values) is the 4th value: \( Q_3 = 219 \) ### Step 3: Calculate the IQR \[ \text{IQR} = Q_3 - Q_1 = 219 - 129 = 90 \] ### Step 4: Determine the Outlier Boundaries - **Lower Bound**: \( Q_1 - 1.5 \times \text{IQR} = 129 - 1.5 \times 90 = 129 - 135 = -6 \) - **Upper Bound**: \( Q_3 + 1.5 \times \text{IQR} = 219 + 1.5 \times 90 = 219 + 135 = 354 \) ### Step 5: Identify Outliers Now we check which values fall outside the range \([-6, 354]\): - All values in the dataset are within this range. ### Conclusion Since all the prices are within the bounds of \(-6\) and \(354\), there are no outliers in the dataset. Thus, the answer is: **none of these**.