Quartiles
 

 

Quartiles

When statistical data is ordered sequentially, the data can be divided into 4 groups of data.   Each of the groups of data is separated by a line called a Quartile. 

Lower quartile line divides the first 25% and second 25% of data.
Middle quartile (also known as the MEDIAN) line divides the 
                         second 25% and third 25% of data. 
Upper quartile line divides the third 25% and fourth 25% of data.

Think of the following words ... Quartile, Quarter, Quart, Quatro.   Each of the previous words comes from concept of the number 4.   We'll look at quarter, quart, and quatro, then, we'll look at Quartiles.

1.    4 quarters make one dollar.
2.   4 quarts make a gallon.
3.   Quatro is the number 4.

Look at the word quartile, assume that quartile relates to the number 4 and we will see how we use it.  Quartile lines are the lines that divide statistical data.   Quartiles break statistical data into 4 pieces. Each of the 4 pieces of data will contain of 25% of the total statistical data.  We use special words to label each of the quartile lines to help describe which of the containers of data we are talking about.  The labels that separate the four groups of data are:

 

(third quartile)  Upper Quartile 

(second quartile)              Median 

(first quartile)  Lower Quartile 

25%

25%

25%

25%

To find the quartiles:

  1.  Median               ... Find the middle of the data from the smallest to largest number of the data.
  2.  Lower Quartile    ... Find the middle (median) of the numbers from the smallest number and the median.
  3.  Upper Quartile    ... Find the middle (median) of the numbers from the median to the largest number of data.

 

Number Set Median

Find the median over the entire set of numbers

 Lower Quartile

Find the median over the numbers below the median

 Upper Quartile

Find the median over the numbers above the median
1, 2, 3, 3, 3, 4, 2, 2, 3, 1, 4, 5 data set used
1,1,2,2,2,3,3,3,3,4,4,5

1,1,2,2

4,4,5
calculation
3+3
2
=  3
1+2
2
=  1.5

= 4
12, 15, 13, 17, 17, 10, 15, 16 data set used
10,12,13,15,15,16,17,17
10,12,13 16,17,17
calculation
15+15
2
=  15

= 12

= 17
93, 96, 100, 75,75, 86, 93,90 data set used
75,75,86,90,93,93,96,100
75,75,86,90 93,93,96,100
calculation
90+93
2
=  91.5
75+86
2
=  80.5
93+96
2
=  94.5
179, 200, 180, 175, 223, 165 data set used
165,175,179,180,200,223
165,175,179 180,200,223
calculation
179+180
2
=  179.5

= 175

= 200
113, 100, 126,142, 125 data set used
100,113,125,126,140
100, 113 126,140
calculation

= 125

100+113
2
=  106.5
126+140
2
=  133

 

Check Your Understanding

For each list of numbers below:

  1. Identify the median in the list.

  2. Identify the lower quartile in the list.

  3. Identify the upper quartile in the list.

  4. Press "Check" to verify your answers.

     

Given this list of numbers What is the lower quartile? What is the upper quartile? What is the median?