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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 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 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.

1 answer

To determine which measure of variability—range or IQR (Interquartile Range)—best describes the spread of Mr. Chang's first period class project grades, let's analyze the dataset:

The grades are: 85, 88, 90, 90, 92, 92, 95, 96, 99.

  1. Range: The range is the difference between the maximum and minimum values. In this dataset:

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

  2. IQR: The IQR is the difference between the first quartile (Q1) and the third quartile (Q3).

    • To find Q1 and Q3, we first need to determine the median:
      • The dataset has 9 points, so the median (5th value) is 92.
    • For Q1 (the median of the first half: 85, 88, 90, 90):
      • Q1 = (88 + 90) / 2 = 89
    • For Q3 (the median of the second half: 92, 95, 96, 99):
      • Q3 = (96 + 99) / 2 = 97.5
    • IQR = Q3 - Q1 = 97.5 - 89 = 8.5

Now let's assess the spread:

  • The distribution is relatively symmetrical with no apparent outliers—grades are clustered toward the higher end but there's no extreme value that distorts the dataset.
  • Given that the dataset does not show skewness or outliers, the IQR is a more robust measure of variability since it is less affected by extreme values and captures the middle 50% of the data.

In conclusion, the best choice from the given options is:

IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.