Interquartile Range Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A data set has Q1=40Q_1 = 40, median =55= 55, Q3=70Q_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.

Solution

  1. 1
    IQR check: IQR=Q3−Q1=70−40=30IQR = Q_3 - Q_1 = 70 - 40 = 30; adding 120 to the upper tail doesn't change Q1 or Q3 if the dataset is large enough, so IQR stays at 30
  2. 2
    Upper fence: Q3+1.5×IQR=70+45=115Q_3 + 1.5 \times IQR = 70 + 45 = 115
  3. 3
    Since 120>115120 > 115, the value 120 is classified as an outlier

Answer

IQR may stay at 30; 120 is an outlier (exceeds upper fence of 115).
The IQR's resistance means extreme values typically don't shift Q1 or Q3 (unless the dataset is very small). This stability is precisely why IQR-based outlier detection is reliable even when new extreme values appear.

About Interquartile Range

The interquartile range (IQR) is Q3−Q1Q3 - Q1 — the spread of the middle 50% of the data, resistant to outliers.

Learn more about Interquartile Range →

More Interquartile Range Examples

Example 1 easy

Calculate the IQR for: [formula] and explain what it measures.

Example 2 medium

Data set A: [formula] and Data set B: [formula]. Compare the range and IQR for both sets and explain

Example 3 easy

A box plot shows [formula] and [formula]. Calculate the IQR and the lower and upper fences for outli

← All Interquartile Range Examples Interquartile Range Concept

Related Concepts

QuartilesBox Plot