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

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

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 determine which option is true about the outliers of the given skewed dataset (5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16), we typically use the interquartile range (IQR) method.

1. **Calculate the Quartiles:**
- Sort the data (already sorted in this case): 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16
- Q1 (first quartile) is the median of the first half of the data: (6+7)/2 = 6.5
- Q3 (third quartile) is the median of the second half of the data: (9+14)/2 = 11.5

2. **Calculate the IQR:**
- IQR = Q3 - Q1 = 11.5 - 6.5 = 5

3. **Determine the outlier boundaries:**
- Lower boundary: Q1 - 1.5 * IQR = 6.5 - 1.5 * 5 = 6.5 - 7.5 = -1
- Upper boundary: Q3 + 1.5 * IQR = 11.5 + 1.5 * 5 = 11.5 + 7.5 = 19

Since the lower boundary is -1 and the upper boundary is 19, this means any data point below -1 or above 19 is considered an outlier. Thus, we check for any values in the original dataset which exceed this range.

- The values of 5, 6, 7, 8, 9, 14, and 16 are all within the bounds of -1 to 19.

Therefore, there are no outliers in this dataset.

So, the correct option is:
**There are no outliers in the dataset.**