Question

Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?(1 point)
Responses

The only outlier of the dataset is 16.
The only outlier of the dataset is 16.

The outliers of the dataset are 14 and 16.
The outliers of the dataset are 14 and 16.

The outliers of the dataset are 5, 14, and 16.
The outliers of the dataset are 5, 14, and 16.

There are no outliers in the dataset.

Answer 1

To determine the outliers in the provided skewed dataset \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\), we can use the Interquartile Range (IQR) method.

1. **Calculate the Quartiles**:
- Sort the data: \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\)
- The median (Q2) is the average of the 6th and 7th values: \((8 + 8) / 2 = 8\).
- Lower half: \(5, 6, 6, 7, 7, 8\); Q1 (Median of lower half) is \((6 + 7) / 2 = 6.5\).
- Upper half: \(8, 8, 9, 9, 14, 16\); Q3 (Median of upper half) is \((9 + 9) / 2 = 9\).

2. **Calculate IQR**:
\[ IQR = Q3 - Q1 = 9 - 6.5 = 2.5 \]

3. **Determine Outlier Boundaries**:
\[
\text{Lower Bound} = Q1 - 1.5 \cdot IQR = 6.5 - 1.5 \cdot 2.5 = 6.5 - 3.75 = 2.75
\]
\[
\text{Upper Bound} = Q3 + 1.5 \cdot IQR = 9 + 1.5 \cdot 2.5 = 9 + 3.75 = 12.75
\]

4. **Identify Outliers**:
- Any value below \(2.75\) or above \(12.75\) is an outlier.
- In your dataset, \(14\) and \(16\) are above \(12.75\) and are therefore outliers.

Thus, the correct response is:

**The outliers of the dataset are 14 and 16.**