Related Positional Measures - Quartiles, Deciles and Percentiles

Related Positional Measures - Quartiles, Deciles and Percentiles :

Besides median there are other measures which divide a series into equal parts.

Important amongest these are quartiles, deciles and percentiles.

Quartiles:

A measure which divides an array into four equal parts is known as quartiles.

Each portion contains equal number of items. The first, second and third points are termed as first quartile (Q₁), second quartile (Q₂) (better named as median) and the third quartile(Q₃). The first quartile (Q₁) or lower quartile, has 25% of the items of the distribution below it and 75% of the items are greater than it. Q₂(median) the second quartile or median has 50 % of the observations above it and 50% of the observations below it. The upper quartile or third quartile(Q₃) has 75% of the items of the distribution below it and 25% of the items are above it. Similarly the other two positional measures can be defined.

(ii)  Deciles:

A measure which divides an array into ten equal parts is known as deciles.

That is Deciles are the values which divides the series into ten equal parts. We get nine dividing positions namely D₁,D₂,…,D ₉ which are called as deciles. Therefore there are nine deciles. It is to be noted that D₅ is equal to median.

(iii) Percentiles:

A measure which divides an array into hundred equal parts is known as Percentiles.

That is percentiles are the values which divides the series into hundred equal parts. We get 99 dividing positions P₁ ,P₂,…,P₉₉ which are called as percentiles. Therefore there are 99 percentiles. It is to be noted that P₅₀ is equal to median.