Which measure of variability—range or IQR—best describes the spread of the dataset?
For a statistics assignment, Shayna randomly surveyed students on how many hours per week they spend playing online games:
1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 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
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 arent any outliers in the dataset
Range; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset
IQR; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset.
To determine the measure of variability that best describes the spread of the dataset, we should consider both the shape of the distribution and the presence of outliers.
Looking at the given dataset, we can observe that the responses are not evenly distributed. There are multiple values that occur more frequently, such as 10.0, 14.0, and 15.0. This suggests a skewed distribution.
Furthermore, we can see that there are outliers in the dataset, such as 2.0, 6.5, and 18.0, which are significantly different from the rest of the responses.
Based on these observations, the measure of variability that best describes the spread of this dataset is the IQR (Interquartile Range). The IQR is less affected by extreme values or outliers than the range. Therefore, the correct answer is:
IQR; the distribution is skewed, and there are outliers in the dataset