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Quartile Calculator
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Quartile Calculator is an online tool for calculating the first quartile, second quartile and third quartile of a set of numbers.

You can see a default numbers given below and click on "Submit". First, divide the set of numbers into three equal groups. Then, quartile is calculated by putting the values in the three formula's of lower, upper and median quartile.
 

Step by Step Calculation

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Step 1 :  

First Quartile Formula


 


If $\frac{1}{4}$ (n + 1) is integer, then first quartile is x$\frac{1}{4}$(n+1)


If $\frac{1}{4}$ (n + 1) is not integer, then first quartile formula is rewritten as:


xinteger($\frac{1}{4}$(n+1)) + (xinteger($\frac{1}{4}$(n+1))+1) (decimal($\frac{1}{4}$(n+1)))


 


Third Quartile Formula


 


If $\frac{3}{4}$ (n+1) is integer, then third quatile is x$\frac{3}{4}$(n+1)


If $\frac{3}{4}$ (n+1) is not integer, then third quartile formula is rewritten as:


xinteger($\frac{3}{4}$(n+1)) + (xinteger($\frac{3}{4}$(n+1))+1)(decimal($\frac{3}{4}$(n+1)))



Step 2 :  

Put the values in a formula and solve it further.



Example Problems

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  1. Determine the first quartile, second quartile and third quartile of the given information of the following sequence 9, 40, 11, 35, 8, 13, 24, 7, 25, 5, 20, 18.


    Step 1 :  

    Given  9, 40, 11, 35, 8, 13, 24, 7, 25, 5, 20, 18.


     


    Arrange the given data in ascending order


     


    5, 7, 8, 9, 11, 13, 18, 20, 24, 25, 35, 40



    Step 2 :  

    Here,


     


    First quartile = $\frac{8+9}{2}$ = $\frac{17}{2}$ = 8.5


     


    Second quartile = $\frac{13+18}{2}$ = $\frac{31}{2}$ = 15.5


     


    Third quartile = $\frac{24+25}{2}$ = $\frac{49}{2}$ = 24.5



    Answer  :  

    8.5 , 15.5 , 24.5



  2. Determine the first quartile, second quartile and third quartile of the given information of the following sequence

    2, 88, 12,49,63,77.


    Step 1 :  

    Given,


     


    2, 88, 12,49,63,77


     


    Arrange the given data in ascending order


     


    2, 12, 49, 63, 77, 88



    Step 2 :  

    Here,


     


    First quartile = $\frac{12}{2}$ = 6


     


    Second quartile = $\frac{49+63}{2}$ = $\frac{112}{2}$ = 56


     


    Third quartile = $\frac{77}{2}$ = 38.5



    Answer  :  

    6, 56, 38.5



More Quartile Calculator
Interquartile Range Calculator Box and Whisker Plot Calculator
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