# Percentiles and Quartiles

Percentiles divide a data set into 100 equal parts. A percentile is simply a measure that tells us what percent of the total frequency of a data set was at or below that measure. For example, let's consider a student's percentile on the ACT. If on this test, a given test taker scored in the 60

As the name suggests, quartiles break the data set into 4 equal parts. The first quartile, Q1, is the 25

Let's look at the following 10 data points.

The range is 100 - 10 = 90. The minimum value is 10, and the maximum value is 100. Because there are ten values (an even number of values), the median is halfway between the 5

What if we were asked for the 25

The first quartile (Q1) is just the "median" of all the values to the left of the true median. We can see that 30 is the middle number of the numbers to the

What if we were asked for the 75

We can summarize all this as follows:

The five values that are bolded are called the 5-number summary, which will be used to create a boxplot, which is another graphical display of the data.

^{th}percentile on the quantitative section, she scored at or better than 60% of the other test takers. Further, if a total of 500 students took the test, she scored at or better than (500)x(.60) = 300 students who took the test. This means that 200 students scored better than she did.As the name suggests, quartiles break the data set into 4 equal parts. The first quartile, Q1, is the 25

^{th}percentile. The second quartile, Q2, is the 50^{th}percentile. The third quartile, Q3, is the 75^{th}percentile. It's important to note that the median is both the 50^{th}percentile and the second quartile, Q2.Let's look at the following 10 data points.

The range is 100 - 10 = 90. The minimum value is 10, and the maximum value is 100. Because there are ten values (an even number of values), the median is halfway between the 5

^{th}and 6^{th}data values, which gives us 55 as the median, or Q2.What if we were asked for the 25

^{th}percentile? We know that the 25^{th}percentile is the first quartile (Q1). It is easy to find the first quartile.The first quartile (Q1) is just the "median" of all the values to the left of the true median. We can see that 30 is the middle number of the numbers to the

**of the true median, so 30 is the 25***left*^{th}percentile and the first quartile (Q1).What if we were asked for the 75

^{th}percentile? We know that the 75^{th}percentile is the third quartile (Q3). The third quartile (Q3) is similarly the "median" of the values to the**of the true median. We can see that 80 is the middle number of the numbers to the right of the true median, so 80 is the 75***right*^{th}percentile and the third quartile (Q3).We can summarize all this as follows:

The five values that are bolded are called the 5-number summary, which will be used to create a boxplot, which is another graphical display of the data.

Related Links:Math Probability and Statistics Boxplot (Box and Whiskers Diagram) Measures of Spread: Range, Standard Deviation, and Variance |

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