← ACARA Digital Technologies Years 9–10

Finding outliers with QUARTILE and the IQR rule

Finds Q1, the value 25% of the way up the data. Use 3 for Q3. IQR = Q3 - Q1. A value more than 1.5 times the IQR below Q1 or above Q3 is flagged as an outlier.

Understanding Finding outliers with QUARTILE and the IQR rule in ACARA Digital Technologies Years 9–10

What it does: If D2 holds Q1 and D4 holds the IQR, then Q1 - 1.5*IQR gives the lower fence. IF with OR checks both fences (F2 lower, G2 upper) and labels the value an outlier if either test is true. The last number is the quartile number: 1 gives Q1, 2 gives the median and 3 gives Q3. It is not a percentage. Use 3 for Q3, the value 75% of the way up the data. IQR = Q3 - Q1. It is the spread of the middle 50% of the data, so you subtract. The lower fence is Q1 - 1.5 x IQR. Check that you use the IQR cell (E3), not the Q3 cell (E2).

Common mistakes: Quart 2 returns the median, not Q3. Q3 needs quart 3, so the line should be =QUARTILE.INC(B2:B100,3). QUARTILE.INC needs a second argument saying which quartile to find. For Q1 it should be =QUARTILE.INC(B2:B100,1).

Class: _____________________  ·  Name: _____________________  ·  Date: _________

Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

This module's key terms are also in a printable crossword (Modules 378–412) and word search (Modules 333–412).

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Each concept is reinforced from every angle — learned, then applied, then tested.

Learning
Duo
Which formula finds Q1 for the data in B2:B100?
=QUARTILE.INC(B2:B100,1)=QUARTILE.INC(B2:B100,25)
Matches
=QUARTILE.INC(B2:B100,2)
↓
Using 2 gives the median (Q2), not Q1. Use 1 for Q1 and 3 for Q3.
Applying
Meanings
Term
=QUARTILE.INC(B2:B100,1)
Meaning
Finds Q1, the value 25% of the way up the data. Use 3 for Q3. IQR = Q3 - Q1. A value more than 1.5 times the IQR below Q1 or above Q3 is flagged as an outlier.
Practice
=QUARTILE.INC(B2:B9,1)-1.5*(QUARTILE.INC(B2:B9,3)-QUARTILE.INC(B2:B9,1))
Testing
Gaps
=(B2:B100,1)
Check Answer
Spots
1D1: =QUARTILE.INC(B2:B100,1)
2D2: =QUARTILE.INC(B2:B100,2)

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Quick Questions

1. Which formula finds Q1 for the data in B2:B100?
A. =QUARTILE.INC(B2:B100,1) ✓
B. =QUARTILE.INC(B2:B100,25)
The last number is the quartile number: 1 gives Q1, 2 gives the median and 3 gives Q3. It is not a percentage.
2. Which formula finds Q3 for the data in B2:B100?
A. =QUARTILE.INC(B2:B100,3) ✓
B. =QUARTILE.INC(B2:B100,75)
Use 3 for Q3, the value 75% of the way up the data.
3. How do you work out the IQR if Q1 is in E1 and Q3 is in E2?
A. =E2-E1 ✓
B. =E2+E1
IQR = Q3 - Q1. It is the spread of the middle 50% of the data, so you subtract.
4. Which formula gives the upper fence if Q3 is in E2 and the IQR is in E3?
A. =E2-1.5*E3
B. =E2+1.5*E3 ✓
The upper fence is Q3 + 1.5 x IQR. Values above it are outliers. Subtracting gives you the lower fence from Q1.
5. Which formula gives the lower fence if Q1 is in E1 and the IQR is in E3?
A. =E1-1.5*E2
B. =E1-1.5*E3 ✓
The lower fence is Q1 - 1.5 x IQR. Check that you use the IQR cell (E3), not the Q3 cell (E2).

Match the Pairs

=QUARTILE.INC(B2:B100,1) → Finds Q1, the value 25% of the way up the data, which is the first step in the IQR rule
=QUARTILE.INC(B2:B100,3)-QUARTILE.INC(B2:B100,1) → Calculates the IQR by subtracting Q1 from Q3
The lower fence is 1.5 times the IQR below Q1. Any value under it is an outlier. → =D2-1.5*D4
Flag a value as an outlier if it is below the lower fence or above the upper fence → =IF(OR(B2<F2,B2>G2),"Outlier","OK")
=QUARTILE.INC(B2:B100,2) → Using 2 gives the median (Q2), not Q1. Use 1 for Q1 and 3 for Q3.
=D3+1.5*D2 → The upper fence should be Q3 + 1.5*IQR, but this adds 1.5 times Q1 instead of the IQR.

Key Term

=QUARTILE.INC(B2:B100,1)
Finds Q1, the value 25% of the way up the data. Use 3 for Q3. IQR = Q3 - Q1. A value more than 1.5 times the IQR below Q1 or above Q3 is flagged as an outlier.

Fill in the Blanks

1. =QUARTILE.INC(B2:B100,1)
Hint: Type the function name that finds a quartile of a data range
2. =QUARTILE.INC(B2:B100,3)
Hint: Type the quartile number that returns the upper quartile, Q3
3. =E2-D2
Hint: Type the operator that finds the IQR from Q3 (in E2) and Q1 (in D2)
4. =D2-1.5*F2
Hint: Type the multiplier used with the IQR to set the lower fence below Q1
5. =IF(OR(B2<G2,B2>H2),"Outlier","OK")
Hint: Type the logical function that is true when a value is beyond either fence

Spot the Error

Question 1
A D1: =QUARTILE.INC(B2:B100,1)
B D2: =QUARTILE.INC(B2:B100,2)
C D3: =D2-D1
Line B — Quart 2 returns the median, not Q3. Q3 needs quart 3, so the line should be =QUARTILE.INC(B2:B100,3).
Question 2
A D1: =QUARTILE.INC(B2:B100)
B D2: =QUARTILE.INC(B2:B100,3)
C D3: =D2-D1
Line A — QUARTILE.INC needs a second argument saying which quartile to find. For Q1 it should be =QUARTILE.INC(B2:B100,1).
Question 3
A D1: =QUARTILE.INC(B2:B100,1)
B D2: =QUARTILE.INC(B2:B100,3)
C D3: =D1-D2
D D4: =D1-1.5*D3
Line C — The IQR is Q3 - Q1. Here Q1 - Q3 would give a negative answer. It should be =D2-D1.
Question 4
A D1: =QUARTILE.INC(B2:B100,1)
B D2: =QUARTILE.INC(B2:B100,3)
C D3: =D2-D1
D D4: =D1-1.5*D2
E D5: =D2+1.5*D3
Line D — The lower fence is Q1 minus 1.5 times the IQR. This line multiplies Q3 (D2) instead of the IQR (D3). It should be =D1-1.5*D3.
Question 5
A D1: =QUARTILE.INC(B2:B100,1)
B D2: =QUARTILE.INC(A2:A100,3)
C D3: =D2-D1
D D4: =D2+1.5*D3
Line B — The data being tested is in column B, but this line reads column A. It should be =QUARTILE.INC(B2:B100,3).

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