Quartiles for even and odd length data set in data mining

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

[quads id=3]