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.
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 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.
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The correct answer is: Range; the distribution is skewed, and there are outliers in the dataset.
The best measure to describe the spread of the given dataset of times for a high school boys' 100-meter race is the range. The range is calculated by subtracting the smallest value from the largest value in the dataset. It gives an overall measure of how spread out the dataset is. In this case, the range of the dataset is 18.0 - 11.0 = 7.0 seconds.
The interquartile range (IQR) is another measure of spread, calculated as the difference between the upper quartile and the lower quartile. However, in this dataset, the IQR would not be the best measure to describe the spread as it is more appropriate for symmetrical distributions and it is not affected by outliers. In this case, the distribution is skewed (not symmetrical) and there are outliers (16.5 and 17.6 seconds), so the IQR is not the best choice.