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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.

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.

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

1 answer

To determine which measure of variability best describes the spread of the dataset, we consider both the nature of the dataset and the characteristics of the measures of variability.

  1. Range measures the difference between the maximum and minimum values. It can be influenced heavily by outliers or extreme values.

  2. Interquartile Range (IQR) measures the range of the middle 50% of the data (between the first quartile (Q1) and the third quartile (Q3)) and is more robust to outliers and skewed data.

Now let's analyze the given dataset:

  • Dataset: 85, 88, 90, 90, 92, 92, 95, 96, 99
  • The minimum is 85 and the maximum is 99, so the range is 99 - 85 = 14.
  • To find the IQR, we need Q1 and Q3.
    • The first quartile (Q1) is the median of the first half (85, 88, 90, 90) = (88 + 90) / 2 = 89.
    • The third quartile (Q3) is the median of the second half (92, 92, 95, 96, 99) = (95 + 96) / 2 = 95.5.
    • Therefore, IQR = Q3 - Q1 = 95.5 - 89 = 6.5.

Now consider the shape of the distribution:

  • The dataset appears relatively symmetrical without extreme outliers. The values are close together, and there's no substantial skewness.

Given that the distribution is symmetrical or close to it and that there are no outliers, the IQR is a suitable measure of variability. The range is less relevant since it can be affected by the minimum and maximum values, which are not extreme in this dataset.

Therefore, the best description of the spread of the dataset is:

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