# Calculate Quartile Items from 1,2,3,4,5

<-- Enter Number Set
<-- Probabilities (or counts for Weighted Average), check box if you are using these →

You entered a number set X of {1,2,3,4,5}

From the 5 numbers you entered, we want to calculate the upper quartile, lower quartile, inner fence points, and outer fence points of that number set:

We need to sort our number set from lowest to highest shown below:
{1,2,3,4,5}

Calculate Upper Quartile (UQ) when y = 75%:
 V = y(n + 1) 100

 V = 75(5 + 1) 100

 V = 75(6) 100

 V = 450 100

V = 4 ← Rounded down to the nearest integer

Upper quartile (UQ) point = Point # 4 in the dataset which is 4
1,2,3,4,5

Calculate Lower Quartile (LQ) when y = 25%:
 V = y(n + 1) 100

 V = 25(5 + 1) 100

 V = 25(6) 100

 V = 150 100

V = 2 ← Rounded up to the nearest integer

Lower quartile (LQ) point = Point # 2 in the dataset which is 2
1,2,3,4,5

Calculate Inter-Quartile Range (IQR):
IQR = UQ - LQ
IQR = 4 - 2
IQR = 2

Calculate Lower Inner Fence (LIF):
Lower Inner Fence (LIF) = LQ - 1.5 x IQR
Lower Inner Fence (LIF) = 2 - 1.5 x 2
Lower Inner Fence (LIF) = 2 - 3
Lower Inner Fence (LIF) = -1

Calculate Upper Inner Fence (UIF):
Upper Inner Fence (UIF) = UQ + 1.5 x IQR
Upper Inner Fence (UIF) = 4 + 1.5 x 2
Upper Inner Fence (UIF) = 4 + 3
Upper Inner Fence (UIF) = 7

Calculate Lower Outer Fence (LOF):
Lower Outer Fence (LOF) = LQ - 3 x IQR
Lower Outer Fence (LOF) = 2 - 3 x 2
Lower Outer Fence (LOF) = 2 - 6
Lower Outer Fence (LOF) = -4

Calculate Upper Outer Fence (UOF):
Upper Outer Fence (UOF) = UQ + 3 x IQR
Upper Outer Fence (UOF) = 4 + 3 x 2
Upper Outer Fence (UOF) = 4 + 6
Upper Outer Fence (UOF) = 10

Calculate Suspect Outliers:
Suspect Outliers are values between the inner and outer fences
We wish to mark all values in our dataset (v) in red below such that -4 < v < -1 and 7 < v < 10
1,2,3,4,5

Calculate Highly Suspect Outliers:
Highly Suspect Outliers are values outside the outer fences
We wish to mark all values in our dataset (v) in red below such that v < -4 or v > 10
1,2,3,4,5