Question

Determine whether the range or interquartile range best describes the spread of a dataset.

The times (in seconds) for a high school boys’ 100-meter race:

11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6 18.0

(1 point)
Responses

Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.

IQR; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.

Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Answer 1

To determine whether the range or interquartile range (IQR) best describes the spread of the dataset, we should first assess the characteristics of the data.

1. **Examine the dataset for outliers**:
- The dataset consists of the following times (in seconds):
11.0, 11.2, 11.7, 12.2, 12.4, 12.6, 12.8, 12.9, 13.1, 13.3, 13.8, 14.2, 14.3, 14.3, 16.5, 17.6, 18.0
- The values are clustered around the lower times (11.0 to 14.3) with a couple of values at the higher end (16.5, 17.6, 18.0), which indicate potential outliers.

2. **Identify if the distribution is skewed**:
- The presence of higher values (16.5, 17.6, 18.0) suggests that the data may be positively skewed.

3. **Use of Range vs. IQR**:
- **Range** is affected by all values in the dataset, including outliers. Since there are outliers present (16.5, 17.6, 18.0), the range would signify a larger spread than the typical data indicates.
- **IQR** considers only the middle 50% of the data and is therefore more robust against outliers and skewed distributions.

Given the characteristics of the dataset—skewness and the presence of outliers—the **IQR** is the better choice to describe the spread of this dataset.

**Thus, the correct response is:**

**IQR; the distribution is skewed, and there are outliers in the dataset.**