Which measure of dispersion describes the range of values in a data set?

Which measure of dispersion describes the range of values in a data set?

• A. IQR
• B. Variance
• C. Standard deviation
• D. Range

Answer: (D)

The appropriate measure of dispersion that describes the range of values in a data set is the range itself. The range is defined as the difference between the largest and smallest values in a data set. It provides a straightforward way to understand the spread or extent of the data. When calculating the range, you simply subtract the minimum value from the maximum value, yielding a single number that reflects the total span of the data set. This is particularly useful for giving a quick sense of how spread out the values are. In contrast, the interquartile range (IQR) measures the middle 50% of the data by calculating the difference between the first and third quartiles. Variance and standard deviation provide information about the average squared distance of each data point from the mean, which focuses more on the distribution of values rather than the simple spread between the highest and lowest points. Thus, while IQR, variance, and standard deviation are all valuable statistics, they serve different purposes and do not describe the overall breadth of values in the same direct way that the range does.

The appropriate measure of dispersion that describes the range of values in a data set is the range itself. The range is defined as the difference between the largest and smallest values in a data set. It provides a straightforward way to understand the spread or extent of the data.

When calculating the range, you simply subtract the minimum value from the maximum value, yielding a single number that reflects the total span of the data set. This is particularly useful for giving a quick sense of how spread out the values are.

In contrast, the interquartile range (IQR) measures the middle 50% of the data by calculating the difference between the first and third quartiles. Variance and standard deviation provide information about the average squared distance of each data point from the mean, which focuses more on the distribution of values rather than the simple spread between the highest and lowest points.

Thus, while IQR, variance, and standard deviation are all valuable statistics, they serve different purposes and do not describe the overall breadth of values in the same direct way that the range does.