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Which measure of variability—range or IQR—best describes the spread of the dataset?

Social studies group project grades (out of 100 points) for Mr. Chang’s first period class

85 88 90 90 92 92 95 96 99

(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.
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 need to analyze the characteristics of the dataset you provided:

Dataset: 85, 88, 90, 90, 92, 92, 95, 96, 99

  1. Finding the Range:

    • Range = Maximum value - Minimum value = 99 - 85 = 14

  2. Finding the IQR:

    • First, we need to determine the quartiles:
      • The median (Q2) is the middle value of the dataset. For this dataset of 9 values, the median is the 5th value, which is 92.
      • The first quartile (Q1) is the median of the first half of the dataset (85, 88, 90, 90). Q1 = (90 + 88) / 2 = 89.
      • The third quartile (Q3) is the median of the second half of the dataset (92, 95, 96, 99). Q3 = (96 + 95) / 2 = 95.5.
    • IQR = Q3 - Q1 = 95.5 - 89 = 6.5.

  3. Distribution Assessment:

    • The dataset does not exhibit strong skewness; it appears to be fairly symmetrical with no outliers.

Conclusion: Given that the distribution does not show any significant skewness or outliers, and since the IQR is less impacted by extremes compared to the range, the IQR is a suitable measure of variability in this case.

Based on this analysis, the best response is: IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.