Deciles

The deciles are the nine values of the variable that divide an ordered data set into ten equal parts.

The deciles determine the values for 10%, 20%... and 90% of the data.

D5 coincides with the median.


Calculating Deciles

1. Order the data from smallest to largest.

2. Look for the place that occupies every decile by means of the expression Decile Formula, in the table of cumulative frequency.

Deciles Formula

Li is the lower limit of the decile class.

N is the sum of the absolute frequency.

Fi-1 is the absolute frequency immediately below the decile class.

ai is the width of the class containing the decile class.

The deciles are independent of the widths of the classes.


Example

Calculate the deciles of the distribution for the following table:

  fi Fi
[50, 60) 8 8
[60, 70) 10 18
[70, 80) 16 34
[80, 90) 14 48
[90, 100) 10 58
[100, 110) 5 63
[110, 120) 2 65
  65  

Calculation of the First Decile

Calculation of the First Decile

First Decile Calculation

Calculation of the Second Decile

Calculation of the Second Decile

Second Decile Calculation

Calculation of the Third Decile

Calculation of the Third Decile

Third Decile Calculation

Calculation of the Fourth Decile

Calculation of the Fourth Decile

Fourth Decile Calculation

Calculation of the Fifth Decile

Calculation of the Fifth Decile

Fifth Decile Calculation

Calculation of the Sixth Decile

Calculation of the Sixth Decile

Sixth Decile Calculation

Calculation of the Seventh Decile

Calculation of the Seventh Decile

Seventh Decile Calculation

Calculation of the Eighth Decile

Calculation of the Eighth Decile

Eighth Decile Calculation

Calculation of the Ninth Decile

Calculation of the Ninth Decile

Ninth Decile Calculation