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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

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 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.

1 answer

To determine which measure of variability best describes the spread of Mr. Chang's first-period class grades (85, 88, 90, 90, 92, 92, 95, 96, 99), we should first analyze the qualities of the dataset:

  1. Range: This is the difference between the highest and lowest values in the dataset. Here, the range is 99 - 85 = 14.

  2. Interquartile Range (IQR): This measures the spread of the middle 50% of the data and is calculated as Q3 - Q1.

    • To find Q1 (the 25th percentile) and Q3 (the 75th percentile):
      • The ordered data set is: 85, 88, 90, 90, 92, 92, 95, 96, 99.
      • Q1 is the median of the first half: (88, 90, 90, 92) → Q1 = 90.
      • Q3 is the median of the second half: (92, 95, 96, 99) → Q3 = 95.
    • Therefore, IQR = Q3 - Q1 = 95 - 90 = 5.

  3. Distribution Shape:

    • The grades are relatively close together, with no extreme values (outliers), and the distribution appears symmetrical, as it is centered around the mean.

Given this analysis:

  • The IQR is a better descriptor of variability when there are outliers or skewed distributions. However, in this case, there are no outliers and the distribution appears symmetrical.

  • The Range gives a measure of total spread, but IQR is generally more robust to outliers.

Considering all these points, the best response from the given options is:

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