# How do you find the interquartile range and outliers?

Table of Contents

## How do you find the interquartile range and outliers?

This is done using these steps:

- Calculate the interquartile range for the data.
- Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers).
- Add 1.5 x (IQR) to the third quartile. Any number greater than this is a suspected outlier.
- Subtract 1.5 x (IQR) from the first quartile.

## How do you find potential outliers?

A value is suspected to be a potential outlier if it is less than (1.5)(IQR) below the first quartile or more than (1.5)(IQR) above the third quartile. Potential outliers always require further investigation.

## How do you find the upper and lower outlier boundaries?

Here are the steps:

- Find the IQR.
- Multiply the IQR by 1.5.
- Add the resulting number to Q3 to get an upper boundary for outliers.
- Subtract the same resulting number (from #2) from Q1 to get a lower boundary for outliers.
- If a number in the data set lies beyond either boundary, it is considered an outlier.

## What is interquartile range example?

The interquartile range is equal to Q3 minus Q1. For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. Q1 is the middle value in the first half of the data set.

## What are the limits for outliers?

Outliers are values below Q1-1.5(Q3-Q1) or above Q3+1.5(Q3-Q1) or equivalently, values below Q1-1.5 IQR or above Q3+1.5 IQR. These are referred to as Tukey fences. For the diastolic blood pressures, the lower limit is 64 – 1.5(77-64) = 44.5 and the upper limit is 77 + 1.5(77-64) = 96.5.

## How do you define outliers in data?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

## How do you find the interquartile range of a data set?

To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

## Why is interquartile range important?

Besides being a less sensitive measure of the spread of a data set, the interquartile range has another important use. Due to its resistance to outliers, the interquartile range is useful in identifying when a value is an outlier. The interquartile range rule is what informs us whether we have a mild or strong outlier.

## How do you calculate Q1 Q2 and Q3?

Quartile Formula:

- Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)
- Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)
- Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)
- Formula for Interquartile range = Q3 (upper quartile) – Q1 (lower quartile)

## How do you classify outliers?

Multiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers.

## What is the equation for an outlier?

If a point is larger than the value of the first equation, the point is an outlier. If a point is smaller than the value of the second equation, the point is also an outlier. If you want to find extreme outliers, the equations are: Q3 + IQR(3) Q1 – IQR(3)

## How to calculate outliers IQR?

Create the Data

## How do you calculate outliers in math?

Determining Outliers. Multiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers.