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)

Question

Responses

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.
There are no outliers in the dataset.

The only outlier of the dataset is 16.

Answer 1

To identify outliers in a skewed dataset, we typically use the interquartile range (IQR) method. Here are the steps to determine the quartiles and outliers for the dataset: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.

1. Order the dataset: The dataset is already ordered.

2. Find the quartiles:

   • First Quartile (Q1): The median of the first half of the data (5, 6, 6, 7, 7, 8). The median is 7.
   • Third Quartile (Q3): 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:

   • 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 the dataset, values 14 and 16 are greater than 13.25, so they are outliers.

Based on this analysis, the correct response is:

The outliers of the dataset are 14 and 16.