Question

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.

Answer 1

To determine which measure of variability best describes the spread of the dataset, we need to consider the nature of the dataset itself—specifically, whether the distribution is symmetrical or skewed and whether there are outliers.

Given dataset: 85, 88, 90, 90, 92, 92, 95, 96, 99

1. **Range**:
- The range is calculated as the difference between the maximum and minimum values.
- Range = 99 - 85 = 14

2. **Interquartile Range (IQR)**:
- The IQR is the difference between the first quartile (Q1) and the third quartile (Q3).
- For this dataset (sorted in ascending order), we split it into quartiles.
- Median (Q2) = 92
- Lower half: 85, 88, 90, 90 (Q1 is the median of this half)
- Upper half: 92, 95, 96, 99 (Q3 is the median of this half)
- Q1 = (88 + 90) / 2 = 89
- Q3 = (95 + 96) / 2 = 95.5
- IQR = Q3 - Q1 = 95.5 - 89 = 6.5

Next, analyze the distribution:
- The values are fairly evenly distributed around the middle of the dataset, and there is no significant skewness.
- No extreme values or obvious outliers are present that would unduly influence the range.

Given the relatively symmetrical spread and absence of significant outliers:

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