Chapters
What Are Quartiles?
Quartiles are a tool we use in statistics that helps us organize groups of previously ordered data.
Quartiles are the three values of the variable that divide a set of ordered data into four equal parts.
and 
determine the values corresponding to 
%, 
%, and 
% of the data. 
coincides with the median.
Calculation of Quartiles
1. We order the data from smallest to largest.
2. We find the position each quartile occupies using the expression 
where 
Odd number of data
Even number of data
Calculation of Quartiles for Grouped Data
First we find the class where is located, where , in the cumulative frequency table.
is the lower limit of the class where the quartile is found.
is the sum of the absolute frequencies.
is the cumulative frequency before the quartile's class.
is the class width.
Example of Quartile Exercise
Calculate the quartiles of the distribution in the table:
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First we will create a new column with the cumulative frequency values:
In the first cell we place the first absolute frequency.
In the second cell we add the value of the previous cumulative frequency plus the corresponding absolute frequency, and so on until the last one, which must equal 
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Calculation of the First Quartile
We find the interval where the first quartile is located by multiplying 
by and dividing by 
.
We look in the cumulative frequency column 
for the interval that contains 
.
The class of 
is:
We will apply the formula for calculating quartiles for grouped data, extracting the following data:
Calculation of the Second Quartile
We find the interval where the second quartile is located by multiplying by and dividing by .
We look in the cumulative frequency column for the interval that contains 
.
The class of is:
We will apply the formula for calculating quartiles for grouped data, extracting the following data:
Calculation of the Third Quartile
We find the interval where the third quartile is located by multiplying 
by and dividing by .
We look in the cumulative frequency column for the interval that contains 
The class of is:
We will apply the formula for calculating quartiles for grouped data, extracting the following data:
Summarize with AI:
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