Practice Interquartile Range in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The interquartile range (IQR) is Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers.
The IQR ignores the extreme 25% on each end, capturing only the spread of the central bulk of data — making it robust when outliers inflate the regular range.
Example 1
easyCalculate the IQR for: \{15, 22, 28, 35, 42, 50, 58, 65\} and explain what it measures.
Example 2
mediumData set A: \{1, 2, 3, 4, 5, 6, 7, 8, 9, 100\} and Data set B: \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}. Compare the range and IQR for both sets and explain why IQR is preferred as a measure of spread.
Example 3
easyA box plot shows Q_1 = 30 and Q_3 = 50. Calculate the IQR and the lower and upper fences for outlier detection.
Example 4
hardA data set has Q_1 = 40, median = 55, Q_3 = 70. A new value of 120 is added. Without recalculating quartiles, explain why the IQR may remain unchanged and identify whether 120 is an outlier.