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 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. Range; 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.
Answers
GPT-4o mini
To determine whether the range or the interquartile range (IQR) best describes the spread of the given dataset, we should analyze the dataset for skewness and the presence of outliers:
Given race times:
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. **Look for outliers:**
- Outliers in this context can be defined as values significantly higher or lower than the rest of the data.
- The times range from 11.0 to 18.0, but the last two times (16.5, 17.6, and 18.0) appear to stand out as noticeably higher than the majority of times.
2. **Identify skewness:**
- The dataset seems to have a concentration of times in the lower range (11.0 to around 14.3) and then a stretching out to the higher end (16.5, 17.6, and 18.0).
- This suggests the distribution is right-skewed.
3. **Choose the appropriate measure:**
- The IQR is less affected by outliers and is better at indicating the spread in the central 50% of the data.
- The range, on the other hand, considers the entire dataset, including extreme values, and can be misleading in the presence of outliers.
Given that we have identified outliers and the distribution is skewed, the IQR would best describe the spread of this dataset.
Therefore, the correct response is:
**IQR; the distribution is skewed, and there are outliers in the dataset.**
Given race times:
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. **Look for outliers:**
- Outliers in this context can be defined as values significantly higher or lower than the rest of the data.
- The times range from 11.0 to 18.0, but the last two times (16.5, 17.6, and 18.0) appear to stand out as noticeably higher than the majority of times.
2. **Identify skewness:**
- The dataset seems to have a concentration of times in the lower range (11.0 to around 14.3) and then a stretching out to the higher end (16.5, 17.6, and 18.0).
- This suggests the distribution is right-skewed.
3. **Choose the appropriate measure:**
- The IQR is less affected by outliers and is better at indicating the spread in the central 50% of the data.
- The range, on the other hand, considers the entire dataset, including extreme values, and can be misleading in the presence of outliers.
Given that we have identified outliers and the distribution is skewed, the IQR would best describe the spread of this dataset.
Therefore, the correct response is:
**IQR; the distribution is skewed, and there are outliers in the dataset.**