Interquartile Range to Detect Outliers in Data

An observation that differs from an overall pattern on a sample dataset is called an outlier.

Outliers

The outliers may suggest experimental errors, variability in a measurement, or an anomaly. The age of a person may wrongly be recorded as 200 rather than 20 Years. Such an outlier should definitely be discarded from the dataset. However, not all outliers are bad. Some outliers signify that data is significantly different from others. For example, it may indicate an anomaly like bank fraud or a rare disease.

Significance of outliers:

• Outliers badly affect the mean and standard deviation of the dataset. These may statistically give erroneous results.
• Most machine learning algorithms do not work well in the presence of outliers. So it is desirable to detect and remove outliers.
• Outliers are highly useful in anomaly detection like fraud detection where the fraud transactions are very different from normal transactions.

What is Interquartile Range IQR?

IQR is used to measure variability by dividing a data set into quartiles. The data is sorted in ascending order and split into 4 equal parts. Q1, Q2, Q3 called first, second and third quartiles are the values which separate the 4 equal parts.

• Q1 represents the 25th percentile of the data.
• Q2 represents the 50th percentile of the data.
• Q3 represents the 75th percentile of the data.

If a dataset has 2n or 2n+1 data points, then
Q2 = median of the dataset.
Q1 = median of n smallest data points.
Q3 = median of n highest data points.

IQR is the range between the first and the third quartiles namely Q1 and Q3: IQR = Q3 – Q1. The data points which fall below Q1 – 1.5 IQR or above Q3 + 1.5 IQR are outliers.

Example:

Assume the data 6, 2, 1, 5, 4, 3, 50. If these values represent the number of chapatis eaten in lunch, then 50 is clearly an outlier. Step by step way to detect outlier in this dataset using Python:

Step 1: Import necessary libraries.

Python3

import numpy as np
import seaborn as sns

Step 2: Take the data and sort it in ascending order.

Python3

data = [6, 2, 3, 4, 5, 1, 50]
sort_data = np.sort(data)
sort_data

Output:

array([ 1,  2,  3,  4,  5,  6, 50])

Step 3: Calculate Q1, Q2, Q3 and IQR.

Python3

Q1 = np.percentile(data, 25, interpolation = 'midpoint')
Q2 = np.percentile(data, 50, interpolation = 'midpoint')
Q3 = np.percentile(data, 75, interpolation = 'midpoint')

print('Q1 25 percentile of the given data is, ', Q1)
print('Q1 50 percentile of the given data is, ', Q2)
print('Q1 75 percentile of the given data is, ', Q3)

IQR = Q3 - Q1
print('Interquartile range is', IQR)

Output:

Q1 25 percentile of the given data is, 2.5
Q1 50 percentile of the given data is, 4.0
Q1 75 percentile of the given data is, 5.5
Interquartile range is 3.0

Step 4: Find the lower and upper limits as Q1 – 1.5 IQR and Q3 + 1.5 IQR, respectively.

Python3

low_lim = Q1 - 1.5 * IQR
up_lim = Q3 + 1.5 * IQR
print('low_limit is', low_lim)
print('up_limit is', up_lim)

Output:

low_limit is -2.0
up_limit is 10.0

Step 5: Data points greater than the upper limit or less than the lower limit are outliers

Python3

outlier =[]
for x in data:
    if ((x> up_lim) or (x<low_lim)):
         outlier.append(x)
print(' outlier in the dataset is', outlier)

Output:

 outlier in the dataset is [50]

Step 6: Plot the box plot to highlight outliers.

Python3

sns.boxplot(data)

Step 7: Following code can also be used to calculate IQR

Python3

from scipy import stats
IQR = stats.iqr(data, interpolation = 'midpoint')
IQR

Output:

3.0

Conclusion:

IQR and box plot are effective techniques to detect outliers in data.