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 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. IQR; the distribution is symmetrical, or close to it, and there aren’t any 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 skewed, and there are outliers in the dataset.
Answers
GPT-4o
To determine whether the range or interquartile range (IQR) best describes the spread of the dataset, we need to consider both the distribution shape and the presence of outliers.
The given dataset of times (in seconds) for a high school boys' 100-meter race is:
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. **Checking for symmetry and outliers:**
- The values 16.5, 17.6, and 18.0 are significantly higher than the other times in the dataset, suggesting the presence of outliers.
- The dataset appears to be skewed to the right, as the larger values are "pulled" away from the rest of the data points.
2. **Appropriate measure of spread:**
- The **Range** is the difference between the maximum and minimum values, which in this case would be 18.0 - 11.0 = 7.0 seconds. However, because the dataset is skewed and contains outliers, the range could be misleading as it would overemphasize the spread due to those outliers.
- The **Interquartile Range (IQR)** focuses on the middle 50% of the data, thereby reducing the influence of outliers and providing a more accurate representation of the spread for a skewed dataset.
Based on the characteristics of the dataset:
- Distribution is skewed.
- Presence of outliers.
Thus, the interquartile range (IQR) is the best measure to describe the spread of this dataset.
So the correct response is:
**IQR; the distribution is skewed, and there are outliers in the dataset.**
The given dataset of times (in seconds) for a high school boys' 100-meter race is:
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. **Checking for symmetry and outliers:**
- The values 16.5, 17.6, and 18.0 are significantly higher than the other times in the dataset, suggesting the presence of outliers.
- The dataset appears to be skewed to the right, as the larger values are "pulled" away from the rest of the data points.
2. **Appropriate measure of spread:**
- The **Range** is the difference between the maximum and minimum values, which in this case would be 18.0 - 11.0 = 7.0 seconds. However, because the dataset is skewed and contains outliers, the range could be misleading as it would overemphasize the spread due to those outliers.
- The **Interquartile Range (IQR)** focuses on the middle 50% of the data, thereby reducing the influence of outliers and providing a more accurate representation of the spread for a skewed dataset.
Based on the characteristics of the dataset:
- Distribution is skewed.
- Presence of outliers.
Thus, the interquartile range (IQR) is the best measure to describe the spread of this dataset.
So the correct response is:
**IQR; the distribution is skewed, and there are outliers in the dataset.**