Outliers Worksheets - Free Printable

To identify outliers in a data set, we use the Interquartile Range (IQR) method. Here's how it works:

Steps to Find Outliers:

1. Order the data from smallest to largest.
2. Find the first quartile (Q1) – the median of the lower half.
3. Find the third quartile (Q3) – the median of the upper half.
4. Compute the IQR:
$$
\text{IQR} = Q3 - Q1
$$
5. Calculate the lower bound and upper bound for outliers:
- Lower Bound = $ Q1 - 1.5 \times \text{IQR} $
- Upper Bound = $ Q3 + 1.5 \times \text{IQR} $
6. Any data point below the lower bound or above the upper bound is considered an outlier.

Let’s go through each problem step by step.

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1) 82, 74, 84, 78, 70, 97, 84, 80, 79

Step 1: Order the data:
70, 74, 78, 79, 80, 82, 84, 84, 97

Step 2: Find Q1 and Q3
- Total values = 9 → Median (Q2) = 80
- Lower half: 70, 74, 78, 79 → Q1 = median of this = (74 + 78)/2 = 76
- Upper half: 82, 84, 84, 97 → Q3 = (84 + 84)/2 = 84

Step 3: IQR = Q3 - Q1 = 84 - 76 = 8

Step 4: Bounds
- Lower = 76 - 1.5×8 = 76 - 12 = 64
- Upper = 84 + 1.5×8 = 84 + 12 = 96

Step 5: Check values outside bounds
- Below 64? No
- Above 96? Only 97 → Outlier

✔ Outliers = 97

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2) 18, 2, 14, 115, 15, 10, 73, 17

Order: 2, 10, 14, 15, 17, 18, 73, 115

Q1: First 4 values: 2,10,14,15 → median = (10+14)/2 = 12
Q3: Last 4: 17,18,73,115 → median = (18+73)/2 = 45.5
IQR = 45.5 - 12 = 33.5

Bounds:
- Lower = 12 - 1.5×33.5 = 12 - 50.25 = -38.25
- Upper = 45.5 + 1.5×33.5 = 45.5 + 50.25 = 95.75

Check values:
- Below -38.25? No
- Above 95.75? 115 → Outlier

✔ Outliers = 115

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3) 11, 5, 16, 6, 20, 4, 40, 8

Order: 4, 5, 6, 8, 11, 16, 20, 40

Q1: First 4: 4,5,6,8 → median = (5+6)/2 = 5.5
Q3: Last 4: 11,16,20,40 → median = (16+20)/2 = 18
IQR = 18 - 5.5 = 12.5

Bounds:
- Lower = 5.5 - 1.5×12.5 = 5.5 - 18.75 = -13.25
- Upper = 18 + 1.5×12.5 = 18 + 18.75 = 36.75

Check values:
- Below -13.25? No
- Above 36.75? 40 → Outlier

✔ Outliers = 40

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4) 24, 52, 86, 83, 44, 49, 57, 41, 44, 55

Order: 24, 41, 44, 44, 49, 52, 55, 57, 83, 86

Q1: First 5: 24,41,44,44,49 → median = 44
Q3: Last 5: 52,55,57,83,86 → median = 57
IQR = 57 - 44 = 13

Bounds:
- Lower = 44 - 1.5×13 = 44 - 19.5 = 24.5
- Upper = 57 + 1.5×13 = 57 + 19.5 = 76.5

Check values:
- Below 24.5? 24 → Yes → Outlier
- Above 76.5? 83, 86 → Both are outliers

✔ Outliers = 24, 83, 86

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5) 41, 11, 35, 5, 23, 27, 94

Order: 5, 11, 23, 27, 35, 41, 94

Q1: First 3: 5,11,23 → median = 11
Q3: Last 3: 35,41,94 → median = 41
IQR = 41 - 11 = 30

Bounds:
- Lower = 11 - 1.5×30 = 11 - 45 = -34
- Upper = 41 + 1.5×30 = 41 + 45 = 86

Check values:
- Below -34? No
- Above 86? 94 → Outlier

✔ Outliers = 94

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6) 36, 58, 75, 61, 69, 98, 58, 70

Order: 36, 58, 58, 61, 69, 70, 75, 98

Q1: First 4: 36,58,58,61 → median = (58+58)/2 = 58
Q3: Last 4: 69,70,75,98 → median = (70+75)/2 = 72.5
IQR = 72.5 - 58 = 14.5

Bounds:
- Lower = 58 - 1.5×14.5 = 58 - 21.75 = 36.25
- Upper = 72.5 + 1.5×14.5 = 72.5 + 21.75 = 94.25

Check values:
- Below 36.25? 36 → Yes → Outlier
- Above 94.25? 98 → Yes → Outlier

✔ Outliers = 36, 98

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7) 7, 19, 60, 55, 12, 15, 26, 9, 3, 22

Order: 3, 7, 9, 12, 15, 19, 22, 26, 55, 60

Q1: First 5: 3,7,9,12,15 → median = 9
Q3: Last 5: 19,22,26,55,60 → median = 26
IQR = 26 - 9 = 17

Bounds:
- Lower = 9 - 1.5×17 = 9 - 25.5 = -16.5
- Upper = 26 + 1.5×17 = 26 + 25.5 = 51.5

Check values:
- Below -16.5? No
- Above 51.5? 55, 60 → Both are outliers

✔ Outliers = 55, 60

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8) 62, 21, 68, 76, 72, 87, 56

Order: 21, 56, 62, 68, 72, 76, 87

Q1: First 3: 21,56,62 → median = 56
Q3: Last 3: 72,76,87 → median = 76
IQR = 76 - 56 = 20

Bounds:
- Lower = 56 - 1.5×20 = 56 - 30 = 26
- Upper = 76 + 1.5×20 = 76 + 30 = 106

Check values:
- Below 26? 21 → Yes → Outlier
- Above 106? No

✔ Outliers = 21

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✔ Final Answers:

1) Outliers = 97
2) Outliers = 115
3) Outliers = 40
4) Outliers = 24, 83, 86
5) Outliers = 94
6) Outliers = 36, 98
7) Outliers = 55, 60
8) Outliers = 21

Let me know if you'd like these summarized in a table!