QUARTILES, DECILES AND PERCENTILES :

 Introduction:

In Statistics, we commonly encounter the concept of the median, which represents the middle value or mean of the two middle values in a dataset. However, there are other essential values that divide data into equal parts for more comprehensive analysis.

Quartiles divide data into four parts, deciles into ten parts, and percentiles into one hundred parts.

 These measures provide valuable insights into the distribution and spread of data, allowing us to analyze specific segments of a dataset with precision. By comprehending quartiles, deciles, and percentiles, we gain a deeper understanding of the patterns and characteristics of our data.

Quartiles:

The values which divide an array (a set of data arranged in ascending or descending order) into four equal parts are called Quartiles.

Calculated by the following formula

Q1=n/4

Q2=2n/4

Q3=3n/4

Practical Example of   Q1

Datasets

1,2,1,1,2,2,3,1,1,1,1,2,2,1,1,1,2,4,1,1

Arrange in Ascending order

1+1+1+1+1+1+1+1+1+1+1+1+2+2+2+2+2+2+3+4 =20

Here, n=20

Q1=n/4 

=20/4 =5

The value of the 5th item is 1, and that one of the 6th item is 1.

Therefore, Q1 Value =1+1/2 

=2/2=1

Q1=1

Here

Deciles:

The values which divide an array into ten equal parts are called deciles.

Calculated by the following formula

D1=n/10

D2=2n/10

         :

         :

D5=5n/10

Practical Example of   D5

Datasets

1,2,1,1,2,2,3,1,1,1,1,2,2,1,1,1,2,4,1,1

Arrange in Ascending order

1,1,1,1,1,,1,1,1,1,1,1,1,2,2,2,2,2,2,3,4 =20

Here, n=20

D5=5n/10

=5(20)/10

=100/10=10

The value of the 10th item is 1, and that one of the 11th value of item is also 1.

Therefore, D5 value =1+1/2

=2/2=1

D5=1

And

Percentiles:

The values which divide an array into one hundred equal parts are called percentiles. 

Calculated by the following formula

P1=n/100

P2=2n/100

         :

         :

P90=90n/100

Practical Example of   P90

Datasets

1,2,1,1,2,2,3,1,1,1,1,2,2,1,1,1,2,4,1,1

Arrange in Ascending order

1,1,1,1,1,,1,1,1,1,1,1,1,2,2,2,2,2,2,3,4 =20

Here, n=20

P90=90n/100

=90(20)/100

=1800/100=18

The value of the 18th item is 2, and that one of the 19th value of item is 3.

Therefore, P90 value =2+3/2

=5/2=2.5

P90=2.5