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

There are no outliers in the dataset.
There are no outliers in the dataset.

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

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

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

Answer 1

To identify outliers in a skewed dataset, we can use the Interquartile Range (IQR) method:

1. **Sort the data**: The data is already sorted: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.

2. **Calculate Q1 (first quartile) and Q3 (third quartile)**:
- Q1 is the median of the first half of the data (5, 6, 6, 7, 7, 8): The median is 7.
- Q3 is the median of the second half of the data (8, 8, 9, 9, 14, 16): The median is 9.5.

3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 9.5 - 7 = 2.5.

4. **Determine the lower and upper bounds for outliers**:
- Lower bound = Q1 - 1.5 * IQR = 7 - 1.5 * 2.5 = 7 - 3.75 = 3.25.
- Upper bound = Q3 + 1.5 * IQR = 9.5 + 1.5 * 2.5 = 9.5 + 3.75 = 13.25.

5. **Identify outliers**:
- Any data point below 3.25 or above 13.25 is considered an outlier. In this dataset:
- 5 is not an outlier (above 3.25).
- 14 is an outlier (above 13.25).
- 16 is an outlier (above 13.25).

Based on this analysis, **the outliers of the dataset are 14 and 16.**

So, the correct response is:

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