Quartiles
The quartiles are the three values of the variable that divide an ordered data set into four equal parts.
Q_{1}, Q_{2} and Q_{3} determine the values for 25%, 50% and 75% of the data.
Q_{2} 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
L_{i} is the lower limit of the quartile class.
N is the sum of the absolute frequency.
F_{i-1} is the absolute frequency immediately below the quartile class.
a_{i} 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:
f_{i} | F_{i} | |
---|---|---|
[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 |