Ask a New Question
Menu

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 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.
IQR; 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.

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

1 answer

To determine which measure of variability (range or interquartile range - IQR) best describes the spread of Shayna's dataset, we first need to analyze the data.

The dataset is:

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

Calculate the Range:

The range is found by subtracting the minimum value from the maximum value.

  • Maximum = 18.0
  • Minimum = 1.0
  • Range = 18.0 - 1.0 = 17.0

Calculate the IQR:

  1. Sort the dataset (already sorted).
  2. Find Q1 (the first quartile) and Q3 (the third quartile).
    • Q1 is the median of the first half of the data: 1.0, 1.0, 2.0, 6.5, 10.0, 10.0, 10.0, 10.0 (median is (6.5 + 10.0) / 2 = 8.25).
    • Q3 is the median of the second half of the data: 12.0, 12.5, 14.0, 14.0, 15.0, 15.0, 15.5, 16.0, 17.5, 18.0 (median is (15.0 + 15.5) / 2 = 15.25).
  3. IQR = Q3 - Q1 = 15.25 - 8.25 = 7.0.

Analyze Distribution:

  • The dataset includes some values that are much lower (1.0, 2.0) and a few higher values, suggesting that the distribution is slightly skewed. Therefore, there are potential outliers. A visual analysis (like a box plot) would typically show that the lowest values are significantly below the rest of the dataset.

Conclusion:

Since the distribution is slightly skewed and potentially contains outliers, the IQR would be a better measure of variability than the range. The IQR is robust against outliers and provides a better representation of the spread of the central portion of the data.

Answer:

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