Quartiles

The quartiles are the three values of the variable that divide an ordered data set into four equal parts.

Q1, Q2 and Q3 determine the values for 25%, 50% and 75% of the data.

Q2 coincides with the median.


Calculating Quartiles

1. Order the data from smallest to largest.

2. Look for the place that occupies every quartile by means of the expression Quartiles Formula, in the table of cumulative frequencies.

Odd Number of Data

2, 5, 3, 6, 7, 4, 9

Finding Quartiles

Even Number of Data

2, 5, 3, 4, 6, 7, 1, 9

Finding Quartiles


Calculation of Quatiles for Grouped Data

Calculation of Quatiles for Grouped Data

Li is the lower limit of the quartile class.

N is the sum of the absolute frequency.

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

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

The quartiles are independent of the widths of the classes.


Example

Calculate the quartiles 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  

Calculating the First Quartile

Calculating the First Quartile

First Quartile Calculation

Calculating the Second Quartile

Calculating the Second Quartile

Second Quartile Calculation

Calculation of the Third Quartile

Calculating the Third Quartile

Third Quartile Calculations