Question

Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8,
8, 8, 9, 9, 14, 16?

• The outliers of the dataset are 14 and 16.
• The only outlier of the dataset is 16.
• There are no outliers in the dataset.
• The outliers of the dataset are 5, 14, and 16.

Answer 1

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

1. **Order the dataset (not needed here, but it's given):**
\[
5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16
\]

2. **Find Q1 (the first quartile) and Q3 (the third quartile):**
- The median (Q2) is the average of the 6th and 7th values:
\[
Q2 = \frac{8 + 8}{2} = 8
\]
- For Q1, the lower half of the data is \(5, 6, 6, 7, 7\):
\[
Q1 = 6
\]
- For Q3, the upper half of the data is \(8, 9, 9, 14, 16\):
\[
Q3 = 9
\]

3. **Calculate the IQR:**
\[
\text{IQR} = Q3 - Q1 = 9 - 6 = 3
\]

4. **Determine the lower and upper bounds for outliers:**
- Lower bound = \(Q1 - 1.5 \times \text{IQR} = 6 - 1.5 \times 3 = 6 - 4.5 = 1.5\)
- Upper bound = \(Q3 + 1.5 \times \text{IQR} = 9 + 1.5 \times 3 = 9 + 4.5 = 13.5\)

5. **Identify outliers:**
- Any data point less than 1.5 or greater than 13.5 is considered an outlier.
- In the dataset, the values \(14\) and \(16\) are greater than \(13.5\), making them outliers.
- The value \(5\) is not considered an outlier since it is greater than \(1.5\).

Based on this analysis, the correct statement is:
- **The outliers of the dataset are 14 and 16.**