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 
, in the table of cumulative frequencies.
Odd Number of Data
2, 5, 3, 6, 7, 4, 9
Even Number of Data
2, 5, 3, 4, 6, 7, 1, 9
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 Second Quartile
Calculation of the Third Quartile
