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
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 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 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 skewed, and there are outliers in the dataset.
To determine whether the range or IQR best describes the spread of the dataset, we should consider the distribution and the presence of outliers.
Looking at the given data:
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
We can see that the data is not evenly distributed and there are some repeated values. However, there are no extreme values that can be considered as outliers.
The range is calculated by subtracting the smallest value from the largest value:
Range = 18.0 - 1.0 = 17.0
This means that the dataset has a range of 17.0.
The interquartile range (IQR) measures the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3):
Q1 = 10.0 (the median of the first half of the data)
Q3 = 15.0 (the median of the second half of the data)
IQR = Q3 - Q1 = 15.0 - 10.0 = 5.0
Comparing the range and IQR values, we can see that the range (17.0) is larger than the IQR (5.0). This indicates that the dataset has more variability in the extreme values (outliers) rather than the middle 50% of the data.
Therefore, the correct answer is: Range; the distribution is skewed, and there are outliers in the dataset.