First Quartile

In this page we are going to discuss about first quartile concept .In statistics , mean , median and mode will give the location of the values. But it doesn't indicate anything about their spread. Among many , one of the method to know the spread is first quartile. to find first quartile, let us follow the following method:

Case 1:

If there is an even number of data, arrange them in ascending order and split them into their lower and upper half. Then take the median of the lower half to get the first quartile. I like to share this Statistics Quartiles with you all through my article.

Case 2:

If there are odd number of data, arrange them in ascending order and remove the median. Now as usual split them into their lower and upper half. Then take the median of the lower half to get the first quartile.

First quartile is denoted by the symbol Q1.

Now let us discuss few problems on this topic find first quartile.


Find first quartile


Below are the examples on find first quartile -

Example 1:

Find the first quartile for the following data: 7 9 12 13 8 11.

Solution : Let us arrange the given data in ascending order which have even number of values

7 8 9 11 12 13

Here the lower half are 7 8 9. The median is 8.

Therefore, the first quartile is 8.

Example 2:

Find the first quartile for the following data: 7 8 22 20 17 18 19 12 13.

Solution : Let us arrange the given data in ascending order which have odd number of values

7 8 12 13 17 18 19 20 22

Here the median is 17. After removing the median 17, the lower half values are 7 8 12 13.

Here the median is `(1/2)` ( 8 + 12) = 10.

Therefore, the first quartile is 10.

Example 3:

Find the first quartile for the following data: 7.6 4.8 1.2 6.9 4.8 7.2 8.1 10.3 4.8 6.7.

Solution : Let us arrange the given data in ascending order which have even number of values

1.2 4.8 4.8 4.8 6.7 6.9 7.2 7.6 8.1 10.3

Here the lower half is 1.2 4.8 4.8 4.8 6.7. The median is 4.8.

Therefore, the first quartile is 4.8. Please express your views of this topic Adding Binary Numbers by commenting on blog.


Practice problems


1. Find first quartile of the following data

9 2 3 10 3 13 6 5

[Answer: Q1 = 2.5]

2. Find first quartile of the following data

2 12 14 8 8 4 2 5

[Answer: Q1 = 3]