The use of quartiles can be essential for you to move forward with your thesis or statistical research project. Although of course, the lack of time can often compromise your work. Don’t worry! In this article we are going to explain in detail what it is and how to calculate the quartiles using his formula and with an example.

Read on for more details!

## What is a statistical quartile and how is it calculated?

To put it simply and concisely, quartiles are measures that, in statistics, allow you to divide values equally and, from that, locate the position of a given value. On a certain amount of values, imagine them as a list or straight line, three points are placed in order to divide it into four, hence its name.

In short, these three points are known as Q1, Q2 and Q3, each of these points keeps a certain percentage of the number of values:

Q1: is the first point to place and takes the first 25% of the sequence of numbers.

Q2: It sits right in the middle, takes 25% from the right and 25% from the left to the next point, so it has 50% of the data volume. It can be obtained in the same way as the statistical median.

Q3: represents the end point and covers the remaining 25%.

The quartiles are part of the so-called quantiles, together with the deciles and percentiles. They are widely used in research related to descriptive statistics and database analysis.

interquartile range

It is called interquartile range to the difference that exists between the third and fourth quartiles, that is, between the spaces behind and in front of Q3. In that particular interval, half of the data is already clustered. By doing an analysis of this tour, you will have information about the dispersion of the sample.

If an interquartile is small, over a larger range, the values become extreme. On the other hand, if both are large, the data tends to spread out, being small, they cluster relative to the central values.

## Quartiles, deciles and percentiles

Before we told you that, in addition to quartiles, there are also other quantiles known as deciles and percentiles, these are other ways of locating and separating data sets. They stand out for:

Deciles: These are numbers that allow dividing the values into ten identical parts, therefore, there are nine points that have to be placed. The sequence goes from D1 to D9.

Percentiles: for this case, the sequence of values is divided into 100 by placing 99 points. The symbology is with the P (P1 to P99).

In this way, it is understood that quartiles, deciles and percentiles are widely applied measures in statistics.

## Formula to calculate Q1, Q2 and Q3

To calculate the quartiles you are going to need a formula that is very easy to use and understand. Before starting with that, it is essential that you order the sequence of numbers that you have from smallest to largest, always before working, it is almost like a law. The formula is the following:

Qa = a (N+1) / 4

In this formula, “Q” represents the quartile and “a” the one you want to obtain, be it 1, 2 or 3. “N”, for its part, symbolizes the number of values or numbers that make up your database. The rest of the data never have to be modified, they are predetermined in the formula.

## Example of obtaining quartiles with their formula

Knowing what a quartile is, what it is for and how to apply it, together with its formula, all that remains is to see a practical example to fully understand how to use and calculate it. Let’s have the following list of numbers:

12, 85, 68, 95, 75, 21, 53, 64, 25, 45

With these numbers, as we indicated before, you will have to rearrange them so that they are from lowest to highest, thus:

12, 21, 25, 45, 53, 64, 68, 75, 85, 95

Now, with this sorted, now it remains to dump the data into the formula that we already showed you:

Q = a (N+1) / 4

Q = 1 (10+1) / 4

Q1 = 2.75

The result is a number decimal, so it is impossible for you to locate the number based on its location. For example, if the result had been 3, a whole, then you locate the number 25 and that’s it, quartile Q1 found. In this case, since it is 2.75, you will have to carry out another calculation to be able to find what number is located exactly in that position, that is, between 2 and 3.

The new calculation implies that Q1 is equal to the number that matches the integer of the result, in this case 21 in position 2, plus the decimal subtraction (0.75) and that multiplied by the difference between the positions in which the decimal result (2 and 3), leaving:

Q1 = 21 + 0.75 (25-21)

Q1 = 24

So, for position 2.75, the number to place is 24.

### Do you need help to finish your work or thesis on statistics?

In Theses and Masters We fully understand that you do not have time to dedicate to this type of activity for your projects. Due to lack of time, it is likely that you cannot take care of yourself, so we can help you. We have more than 10 years of experience providing our service of drafting and academic advising.

We have a team made up of more than 500 professionals specialized in all academic areas. We can assign you an advisor specialized in your type of project and career, so the quality of your project will never be compromised. We work based on partial deliveries, considering your final delivery date.

We guarantee an original work thanks to the use of turnitin, the powerful anti-plagiarism detector. It has very powerful internal databases, which allows us to detect all types of existing plagiarism, including paraphrased. Our service is confidential, we will never reveal your personal information to anyone.

#### Request your free estimate right now!

Do not hesitate to request your budget free of charge through our main communication channels with the client, such as:

WhatsApp: A web advisor will answer you to clear up all the doubts you have about our service and, in addition, start the budgeting process.

Web form: Fill out the form that you will see at the end of the article so that we can contact you as soon as possible.

We have many means of payment enabled for you, contact us to finish your quartile statistics project at once.