Mia has taught math and science and has a Master's Degree in Secondary Teaching.
In this lesson, you'll learn the definition of lower quartile and what it represents in a set of data. You'll review a few examples and follow the steps of finding the lower quartile, then you can take a brief quiz to test what you've learned.
Quarters & Quartiles
To understand what the lower quartile is, we first need to understand what a quartile is. The root of the word quartile is 'quart,' which means one fourth. When we're dividing a set of data into quartiles, we're doing the same thing as dividing a dollar into four quarters. Or, if you are a sports fan, you can think of each quarter of a basketball game. The lower quartile is the first fourth, or the lowest 25%, of the data. It's like the first quarter of a basketball game.
To find the lower quartile of a set of data, we can find the median of the data and then find the median of the first half. This strategy is similar to dividing a cake into halves, and then dividing one of the halves in half so that you end up with a quarter of the cake.
Another strategy involves using the following formula, where Q1 is the lower quartile and n is the number of values in the set of data. This formula does not give you the value of the lower quartile, but tells you what term it is in when the data is ordered:
We are given the following set of data. Let's find the lower quartile:
3, 5, 7, 9, 14, 16, 22
Using the first strategy, we would first find the median of the entire set of data, which is 9. Then we would find the median of the values below 9. That would leave us 5 as our lower quartile.
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Using the formula, we would substitute 7 for n because we have 7 values in our data set. Completing the calculation, ¼(7 + 1), gives us 2. That tells us that the 2nd term is the lower quartile. The second term is 5.
As you can see, both strategies will give you the same value.
How would we find the lower quartile of these values:
5, 14, 9, 6, 15, 7, 2, 0, 7, 8, 19
Notice that these values are not ordered. We must put them in order first!
0, 5, 6, 7, 7, 8, 9, 14, 15, 19
Let's use the formula to find the lower quartile. There are 11 values, so we substitute 11 for n in the formula. That gives us ¼(11 + 1) = 3. The lower quartile is the third term, which is 6.
Let's take a moment or two to quickly recap the important information that we've learned here. We learned that a quartile basically means one fourth, and that therefore, the lower quartile, Q1, represents the lowest 25% of a data set. It can be found by finding the median of the lower half of the data. It can also be found by using the formula:
which tells you what term of the data set represents the lower quartile.
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