## Quartiles

Quartiles are set of 3 values(points) that divides a set into four equal parts(quarters).

The three points are as follows:

• The given set should be arranged in order(either ascending or descending).
• Median (Q2) is the middle value of the given set.

Q2 = 1/2(n+1)th value, where n is the total number of elements in the given set.

• Lower quartile(Q1) is the middle value of the lower half of given set.

Q1= 1/4(n+1)th value,  where n is the total number of elements in    the set.

• Upper quartile (Q3) is the median of the upper half of the given set.

Q3 = 3/4(n+1)th value, where n is the total number of elements in the given set.

Example 1. Find the  quartiles of the following set {3,2,5,4,4,7,2}.

Solution:

• Let us arrange in ascending order. 2,2,3,4,4,5,7.
• Since there are 7 elements in the set, the

lower quartile Q1 = (7+1)/4th value,

= 8/4thvalue

= 2nd value of the given set.

So Q1 = 2.

• Median = (7+1)/2 th value

= 8/2th value

= 4th value of the set

So Q2 =  4

• Upper quartile Q3 = 3/4(n+1)th value

= 3/4(8) th value

= 6 th value of the given set

So Q3 = 5.

Example 2: Find the median, upper quartile, and lower quartile of the given set {21, 25 22, 22, 20, 26, 23, 24, 24}

Solution:

• Arrange the given set in order

20, 21, 22, 22, 23, 24, 24, 25, 26.

• Since there are 9 elements in the set n=9.
• The lower quartile Q1 = (9+1)/4 th value

= 10/4 th value

= 2.5 th value, since we can not take the 2.5th value

we will take Q1 as the average of 2nd and 3rd value

Q1  = Average of 2nd and 3rd value

= (21+22)/2

= 21.5

• The median Q2         = (9+1)/2 th valule

=   10/2 th value

=  5th value

Q2        =  23

• The upper quartile Q3 = 3(9+1)/4 th value

= 3/4(10)th value

= 7.5 th value

= Average of 7 and 8th value

= (24+25)/2

Q3   = 24.5

Quartiles to Basic statistics