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 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.
Range; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is skewed, and there are outliers in the dataset.
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IQR; the distribution is skewed, and there are outliers in the dataset.
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Range; the distribution is skewed, and there are outliers in the dataset.
To determine whether the range or interquartile range best describes the spread of a dataset, we need to analyze the characteristics of the dataset.
Looking at the times for the 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
We can observe that the distribution is not symmetrical, as there is a concentration of shorter times on the left side and a few longer times on the right side.
Additionally, there are outliers in the dataset, as the times 16.5, 17.6, and 18.0 are significantly higher than the rest of the data.
Given these characteristics, the interquartile range (IQR) would be a better measure of describing the spread of the dataset. The IQR captures the range of the middle 50% of the data, which is generally more reliable when outliers are present or the distribution is skewed.