Question

Explain how removing a "0" from a dataset will impact the interquartile range. Will it increase or decrease or stay the same?

Answer 1

Short answer: It can do any of the three — increase, decrease, or stay the same. Which happens depends on where the 0 sits in the ordered data relative to the first and third quartiles and on the sample size (removing one value changes ranks and can move the quartile positions).

Reason: IQR = Q3 − Q1. Removing a data point can change Q1 and/or Q3 (because it changes the order statistics), so the IQR may go up, down, or not change.

Examples (using the usual “median-of-halves” quartile rule):
- IQR unchanged:
- Data: [0,1,2,3,4,5,6,7] → Q1=1.5, Q3=5.5, IQR=4.
- Remove 0 → [1,2,3,4,5,6,7] → Q1=2, Q3=6, IQR=4.
- IQR decreases:
- Data: [0,0,1,2,3] → Q1=0, Q3=2.5, IQR=2.5.
- Remove one 0 → [0,1,2,3] → Q1=0.5, Q3=2.5, IQR=2.0.
- IQR increases:
- Data: [0,1,1,1,1,1,1,10,100] → Q1=1, Q3=1, IQR=0.
- Remove 0 → [1,1,1,1,1,1,10,100] → Q1=1, Q3=5.5, IQR=4.5.

Note: quartile computation rules differ slightly between software/packages, but the qualitative conclusion (can increase, decrease, or stay the same) does not change. In large samples, removing a single extreme value outside the middle 50% often leaves the IQR unchanged.