The following 11 scores were input in the gradebook for Prof. Williams's class. $$ 73,74,75,83,85,86,88,91,92,92,195 $$ 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".

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We first order the data (which is already in increasing order):

$$
73,\,74,\,75,\,83,\,85,\,86,\,88,\,91,\,92,\,92,\,195
$$

**Step 1: Identify the median (Q2).**

There are 11 numbers, so the median is the 6th number:

$$
\text{Median} = 86
$$

**Step 2: Determine Q1 and Q3.**

The lower half (excluding the median) is:

$$
73,\,74,\,75,\,83,\,85
$$

The median of this set is the 3rd number:

$$
Q1 = 75
$$

The upper half (excluding the median) is:

$$
88,\,91,\,92,\,92,\,195
$$

The median of this set is the 3rd number:

$$
Q3 = 92
$$

**Step 3: Calculate the interquartile range (IQR).**

$$
\text{IQR} = Q3 - Q1 = 92 - 75 = 17
$$

**Step 4: Determine the fences for outliers.**

The lower fence is:

$$
\text{Lower Fence} = Q1 - 1.5 \times \text{IQR} = 75 - 1.5 \times 17 = 75 - 25.5 = 49.5
$$

The upper fence is:

$$
\text{Upper Fence} = Q3 + 1.5 \times \text{IQR} = 92 + 1.5 \times 17 = 92 + 25.5 = 117.5
$$

**Step 5: Identify the outliers.**

Any score below $$49.5$$ or above $$117.5$$ is an outlier. Checking the dataset, the only value above $$117.5$$ is:

$$
195
$$

Thus, the outlier is $$195$$.
The outlier is 195.

The following 11 scores were input in the gradebook for Prof. Williams's class. \[ 73,74,75,83,85,86,88,91,92,92,195 \] 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".

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