Question
Determine if there are any outliers in the skewed dataset 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25. Enter the number of the correct option.
Option #1: There are no outliers in the dataset.
Option #2: The value 25 is the only outlier in the dataset.
Option #3: The values 25 and 19 are the only two outliers in the dataset.
Option #4: The values 25, 19, and 15 are the only three outliers in the dataset.
(1 point)
The accurate statement is Option #
.
Option #1: There are no outliers in the dataset.
Option #2: The value 25 is the only outlier in the dataset.
Option #3: The values 25 and 19 are the only two outliers in the dataset.
Option #4: The values 25, 19, and 15 are the only three outliers in the dataset.
(1 point)
The accurate statement is Option #
.
Answers
GPT-4o mini
To determine if there are any outliers in the dataset (11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25), we can use the Interquartile Range (IQR) method.
1. **Calculate the Quartiles**:
- The first step is to find the median (Q2). The dataset is already sorted, and the median for an odd number of observations is the middle number:
- Median (Q2) = 13 (the 6th value in the list).
2. **First Quartile (Q1)**:
- Q1 is the median of the lower half of the dataset (11, 12, 12, 13, 13).
- Q1 = 12 (the 3rd value).
3. **Third Quartile (Q3)**:
- Q3 is the median of the upper half of the dataset (14, 14, 15, 19, 25).
- Q3 = 15 (the 3rd value).
4. **Calculate the Interquartile Range (IQR)**:
- \( IQR = Q3 - Q1 = 15 - 12 = 3 \).
5. **Determine the Outlier Boundaries**:
- Outlier boundaries are:
- Lower Bound = \( Q1 - 1.5 \times IQR = 12 - 1.5 \times 3 = 12 - 4.5 = 7.5 \).
- Upper Bound = \( Q3 + 1.5 \times IQR = 15 + 1.5 \times 3 = 15 + 4.5 = 19.5 \).
6. **Identify Outliers**:
- Any value below 7.5 or above 19.5 is considered an outlier.
- In the dataset, 25 is above 19.5 and is thus an outlier.
- The value 19 is within the boundaries (7.5 to 19.5), so it's not an outlier.
Based on the analysis, the only outlier in the dataset is the value 25.
Therefore, the accurate statement is Option #2: The value 25 is the only outlier in the dataset.
1. **Calculate the Quartiles**:
- The first step is to find the median (Q2). The dataset is already sorted, and the median for an odd number of observations is the middle number:
- Median (Q2) = 13 (the 6th value in the list).
2. **First Quartile (Q1)**:
- Q1 is the median of the lower half of the dataset (11, 12, 12, 13, 13).
- Q1 = 12 (the 3rd value).
3. **Third Quartile (Q3)**:
- Q3 is the median of the upper half of the dataset (14, 14, 15, 19, 25).
- Q3 = 15 (the 3rd value).
4. **Calculate the Interquartile Range (IQR)**:
- \( IQR = Q3 - Q1 = 15 - 12 = 3 \).
5. **Determine the Outlier Boundaries**:
- Outlier boundaries are:
- Lower Bound = \( Q1 - 1.5 \times IQR = 12 - 1.5 \times 3 = 12 - 4.5 = 7.5 \).
- Upper Bound = \( Q3 + 1.5 \times IQR = 15 + 1.5 \times 3 = 15 + 4.5 = 19.5 \).
6. **Identify Outliers**:
- Any value below 7.5 or above 19.5 is considered an outlier.
- In the dataset, 25 is above 19.5 and is thus an outlier.
- The value 19 is within the boundaries (7.5 to 19.5), so it's not an outlier.
Based on the analysis, the only outlier in the dataset is the value 25.
Therefore, the accurate statement is Option #2: The value 25 is the only outlier in the dataset.