Question

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 5, 14, and 16. The outliers of the dataset are 5, 14, and 16. The outliers of the dataset are 14 and 16. The outliers of the dataset are 14 and 16. There are no outliers in the dataset.

Answer 1

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

1. **Find the Quartiles:**
- The dataset in order is \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\).
- The median (Q2) is the average of the 6th and 7th numbers:
\[
Q2 = \frac{8 + 8}{2} = 8
\]

- For Q1 (the first quartile), find the median of the first half of the dataset \(5, 6, 6, 7, 7\):
\[
Q1 = 6
\]
- For Q3 (the third quartile), find the median of the second half of the dataset \(8, 8, 9, 9, 14, 16\):
\[
Q3 = \frac{9 + 9}{2} = 9
\]

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

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

4. **Identify outliers:**
- Any value below 1.5 or above 13.5 is considered an outlier.
- The dataset contains:
- 5, which is greater than 1.5 (not an outlier)
- 14 and 16, which are both greater than 13.5 (both are outliers)

From the analysis, the outliers in the dataset are **14 and 16**.

Therefore, the correct response is: **The outliers of the dataset are 14 and 16.**