Quartiles for even and odd length data set in data mining

By Prof. Fazal Rehman Shamil
Last modified on January 11th, 2020

What is quartile?

Quartile means four equal groups. 

How to find quartiles of odd length data set?

Example:

Data = 8, 5, 2, 4, 8, 9, 5

Step 1:

First of all, arrange the values in order.

After ordering the values:

Data = 2, 4, 5, 5, 8, 8, 9

[quads id=1]

Step 2:

For dividing this data into four equal parts, we needed three quartiles.

Q1: Lower quartile

Q2: Median of the data set

Q3: Upper quartile

Step 3:

Find the median of the data set and label it as Q2.

Data = 2, 4, 5, 5, 8, 8, 9

Q1: 4 – Lower quartile

Q2: 5 – Middle quartile

Q3: 8 – Upper quartile

Inter Quartile Range= Q3 – Q1

                                  = 84

                                  = 4 

What is Outlier?

The outlier is the set of data far away from the common and famous pattern.

How to find outliers?

Outlier is mostly a value higher or lower than 1.5 * IQR

=1.5 * IQR

=1.5 * 5

= 7.5

Population size:

Population size is the total number of values in data.

 

[quads id=2]


How to find quartiles of even length data set?

Example:

Data = 8, 5, 2, 4, 8, 9, 5,7

Step 1:

First of all, arrange the values in order

After ordering the values:

Data = 2, 4, 5, 5, 7, 8, 8, 9

Step 2:

For dividing this data into four equal parts, we needed three quartiles.

Q1: Lower quartile

Q2: Median of the data set

Q3: Upper quartile

Step 3:

Find the median of the data set and label it as Q2.

Data = 2, 4,   ♦    5, 5,     ♦    7, 8    ♦    8, 9

Minimum: 2

Q1:  4 + 5 / 2 = 4.5    Lower quartile

Q2:  5+ 7 / 2 = 6        Middle quartile

Q3:  8 + 8 / 2 = 8       Upper quartile

Maximum: 9

Inter Quartile Range= Q3 – Q1

= 8 –  4.5

= 3.5

Outlier is mostly a value higher or lower than 1.5 * IQR

=1.5 * IQR

=1.5 * 3.5

= 5.25

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