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}

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

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

IQR = UQ - LQ

IQR = 4 - 2

IQR = 2

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

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

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

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

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

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