Question

Identify all values, if any, in the data set that would be considered outliers when creating a modified boxplot
71 74 78 79 79 80 82
1)71
2)82
3)71 and 82
4)no outliers

Answer 1

To identify outliers using a modified boxplot, we first need to find the quartiles and the interquartile range (IQR) of the dataset.

Here’s the dataset: 71, 74, 78, 79, 79, 80, 82.

1. **Order the dataset**: The values are already in order: 71, 74, 78, 79, 79, 80, 82.

2. **Determine Q1, Q2 (median), and Q3**:
- **Q1 (first quartile)**: The median of the first half (71, 74, 78) is 74.
- **Q2 (median)**: The median of the entire dataset is 79.
- **Q3 (third quartile)**: The median of the second half (79, 80, 82) is 80.

3. **Calculate the IQR**:
- **IQR = Q3 - Q1 = 80 - 74 = 6**.

4. **Determine the lower and upper bounds for outliers**:
- **Lower bound = Q1 - 1.5 * IQR = 74 - 1.5 * 6 = 74 - 9 = 65**.
- **Upper bound = Q3 + 1.5 * IQR = 80 + 1.5 * 6 = 80 + 9 = 89**.

5. **Identify outliers**: Outliers are values below the lower bound or above the upper bound.
- Values below 65 and above 89 are considered outliers.

In this dataset, all values (71, 74, 78, 79, 79, 80, 82) are within the bounds of 65 and 89. Therefore, there are no outliers.

The answer is:
4) no outliers.