I just I learned recently about the lower quartile and i am confused on how to do it can someone explain.

Question

Evan though my math teacher went over it i am still confused

Answer 1

Hey Aubrey,

I'd love to help explain.

The lower quartile is similar to the median! The difference is that instead of finding the value in the middle (50%) of a set of numbers, we are finding the value that is located at 1/4 of the set of numbers (25%).

Here is an example of a set:

1,3,6,8,10,11,15,18,19

An easy way to find the lower quartile is to first find the median of the whole set, and then again find the median of the lower half of the set. This will give us the 25th percentile of the set. We can know the median by finding the value in the middle of a set.

In this case, the median is 10. We know this because there are 4 numbers on either side of 10! (Remember that in sets with an odd number of values, the median will always be an actual number in the set, while sets with an even number of values will have a median in between two values of the set). In this case we have an odd number of values (9) so we know that we are correct so far.

Now that we know the median, we can look at the lower half of the set which is:

1,3,6,8

Now we just need to find the median of this lower half! This time, since we have an even number of values (4) the midpoint of this set is between the two middle numbers of 3 and 6. To find the lower quartile, we'll need to take the average (or mean) of these two values. This is done by adding the two numbers together, and the dividing the result by two. When do this, we get 3 + 6 = 9. And 9÷2 = 4.5.

So the lower quartile is 4.5!

Hope this makes sense for you. Let me know if you have any questions.

Tyler