A bakery sells 11 types of sandwiches. Here are their calorie amounts. \[ 280,593,594,599,611,616,617,617,618,619,946 \] Identify all values that are outliers. If there is more than one outlier, separate them with commas. If there are no outliers, click on "None".

We start by sorting the given calorie amounts: \[ 280,\ 593,\ 594,\ 599,\ 611,\ 616,\ 617,\ 617,\ 618,\ 619,\ 946 \] **Step 1: Find the Median (Q2).** With 11 numbers, the median is the 6th value: \[ Q2 = 616 \] **Step 2: Find the First Quartile (Q1).** The lower half (excluding the median) is: \[ 280,\ 593,\ 594,\ 599,\ 611 \] The median of these 5 numbers (the 3rd value) is: \[ Q1 = 594 \] **Step 3: Find the Third Quartile (Q3).** The upper half (excluding the median) is: \[ 617,\ 617,\ 618,\ 619,\ 946 \] The median of these 5 numbers (the 3rd value) is: \[ Q3 = 618 \] **Step 4: Compute the Interquartile Range (IQR).** \[ \text{IQR} = Q3 - Q1 = 618 - 594 = 24 \] **Step 5: Determine the Outlier Boundaries.** - Lower bound: \[ Q1 - 1.5 \times \text{IQR} = 594 - 1.5(24) = 594 - 36 = 558 \] - Upper bound: \[ Q3 + 1.5 \times \text{IQR} = 618 + 1.5(24) = 618 + 36 = 654 \] **Step 6: Identify Outliers.** An outlier is any value below 558 or above 654. Checking the list: - \(280 < 558\), so \(280\) is an outlier. - \(946 > 654\), so \(946\) is an outlier. - All other values lie within the interval \([558, 654]\). **Final Answer:** \(280,946\)