In which situation is the interquartile range (IQR) the preferred measure of spread?

In which situation is the interquartile range (IQR) the preferred measure of spread?

• A. When data contain outliers
• B. When data are perfectly normally distributed
• C. When the sample size is very small
• D. When the data are categorical

Answer: (A)

Interquartile range is a measure of spread that uses the middle 50% of the data, calculated from the first and third quartiles. Because it relies on these quartiles rather than every data point, extreme values have little effect on it. This makes the IQR especially suitable when the data contain outliers or are skewed, since outliers can dramatically distort the standard deviation and the mean. In contrast, if the data are perfectly normal, the standard deviation is typically preferred because it efficiently summarizes spread under that distribution. Very small samples can make quartile estimates unstable, reducing the reliability of the IQR, and if the data are categorical, there isn’t a meaningful way to compute quartiles. So the situation where the data contain outliers is when the IQR is the best choice.

Interquartile range is a measure of spread that uses the middle 50% of the data, calculated from the first and third quartiles. Because it relies on these quartiles rather than every data point, extreme values have little effect on it. This makes the IQR especially suitable when the data contain outliers or are skewed, since outliers can dramatically distort the standard deviation and the mean.

In contrast, if the data are perfectly normal, the standard deviation is typically preferred because it efficiently summarizes spread under that distribution. Very small samples can make quartile estimates unstable, reducing the reliability of the IQR, and if the data are categorical, there isn’t a meaningful way to compute quartiles. So the situation where the data contain outliers is when the IQR is the best choice.