Question

When would the interquartile range serve as a better measure of spread than the standard deviation or range?

A. When data values are spread evenly over a large range of numbers
B. When data values are spread evenly over a small range of numbers
C. When most data values are relatively close to each other
D. When most data values are relatively close to each other but outliers exist

Answer 1

The interquartile range is a better measure of spread than standard deviation when data values are close to each other but outliers are present.

Step-by-step explanation:

The interquartile range (IQR) serves as a better measure of spread than the standard deviation when most data values are relatively close to each other but outliers exist. This scenario corresponds to option D in the provided question. The IQR specifically measures the spread of the middle 50 percent of the data by subtracting the first quartile (Q1) from the third quartile (Q3). Unlike the standard deviation or range, the IQR is less affected by extremes and outliers which can distort the perceived variability of the data collection.