Module 9 · Lesson 18 of 22

Quartiles, interquartile range, and mean deviation

Learning objectives

Compute quartiles, IQR and mean absolute deviation in a free spreadsheet.
Use robust summaries for skewed garment data.
Flag exploratory outliers without automatic deletion.

Core idea

Quartiles split ordered data into four parts; IQR = Q3 − Q1 summarises the middle 50%; mean absolute deviation is the mean distance from a declared centre.

Spreadsheet lab

Q1 = =QUARTILE.INC(A2:A31, 1); Q3 = =QUARTILE.INC(A2:A31, 3).
IQR = Q3 − Q1.
MAD (about mean) = =AVERAGE(ABS(A2:A31 - AVERAGE(A2:A31))) entered as array.
Outlier fences (exploratory only): below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.

Garment-factory example

Repair minutes per garment on a skewed style: Q1 = 3.0, median = 4.5, Q3 = 8.0 → IQR = 5.0. Points beyond Q3 + 1.5·IQR = 15.5 are flagged for cause investigation, not deleted.

Method

Choose median/IQR when data are skewed.
State the quartile convention (inclusive vs exclusive).
Investigate flagged points; delete only with cause.

Common mistakes

Deleting flagged points to make results 'look nicer'.
Using different quartile conventions between reports.

Knowledge check

Pick one answer per question. Explanations appear after you submit.

1. Which pair of functions produce Q1 and Q3?
- =SMALL(range,1), =LARGE(range,1)
- =QUARTILE.INC(range,1), =QUARTILE.INC(range,3)
- =MEDIAN(range), =AVERAGE(range)
- =STDEV.S(range), =VAR.S(range)
2. A point beyond Q3 + 1.5·IQR should be:
- Deleted automatically.
- Flagged for investigation.
- Averaged with the median.
- Replaced with the mean.

Author: Sanjeewa Dehiwalage · Last reviewed: 2026-07-21