Which of the following statements is true about the interquartile range $\mathrm{IQR}$?

• A. The $\mathrm{IQR}$ is affected by extreme outliers in the data.
• B. The $\mathrm{IQR}$ measures the spread of the middle 50% of the data.
• C. The $\mathrm{IQR}$ is always equal to the standard deviation.
• D. The $\mathrm{IQR}$ is calculated as the difference between the maximum and minimum values.

Answer: (B)

Verified step by step guidance

1. Understand what the interquartile range (IQR) represents: it measures the spread of the middle 50% of the data by focusing on the central portion of the dataset.
2. Recall that the IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), so the formula is \(\text{IQR} = Q_3 - Q_1\).
3. Recognize that because the IQR only considers the middle 50% of the data, it is resistant to extreme values or outliers, meaning it is not affected by them.
4. Compare the IQR to other measures of spread, such as the standard deviation, which takes into account all data points and can be influenced by outliers; thus, the IQR is not always equal to the standard deviation.
5. Note that the IQR is not calculated as the difference between the maximum and minimum values; that difference is called the range, which measures the total spread of the data.