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.
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.
To determine whether the range or interquartile range best describes the spread of a dataset, we need to analyze the dataset provided:
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
Looking at the dataset, we can see that there is a noticeable difference between the lowest value (11.0) and the highest value (18.0). Therefore, the range, which is the difference between the maximum and minimum values, can provide an idea of the spread of the dataset.
However, it's important to consider other factors such as the distribution shape and the presence of outliers. In this case, the dataset appears to be almost symmetrical with a slight skew to the right. Additionally, there aren't any extreme values that could be considered as outliers.
Based on these observations, it is more appropriate to use the interquartile range (IQR) to describe the spread of the dataset. The interquartile range represents the range between the first quartile (25th percentile) and the third quartile (75th percentile), and it provides a measure of the spread that is less sensitive to extreme values.
Therefore, the correct answer is: IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.