# 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 8 8 10 18 16 34 14 48 10 58 5 63 2 65 65

#### Calculating the First Quartile  #### Calculating the Second Quartile  #### Calculation of the Third Quartile  