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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.

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.

1 answer

To determine whether the range or interquartile range (IQR) best describes the spread of the dataset, we should first assess the characteristics of the data.

  1. Examine the dataset for outliers:

    • The dataset consists of the following times (in seconds): 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
    • The values are clustered around the lower times (11.0 to 14.3) with a couple of values at the higher end (16.5, 17.6, 18.0), which indicate potential outliers.

  2. Identify if the distribution is skewed:

    • The presence of higher values (16.5, 17.6, 18.0) suggests that the data may be positively skewed.

  3. Use of Range vs. IQR:

    • Range is affected by all values in the dataset, including outliers. Since there are outliers present (16.5, 17.6, 18.0), the range would signify a larger spread than the typical data indicates.
    • IQR considers only the middle 50% of the data and is therefore more robust against outliers and skewed distributions.

Given the characteristics of the dataset—skewness and the presence of outliers—the IQR is the better choice to describe the spread of this dataset.

Thus, the correct response is:

IQR; the distribution is skewed, and there are outliers in the dataset.