The **quartiles** are those points that are taken from the regular intervals of the function of a random variable. They are used continuously in various particular survey and sales data to classify and divide populations into parts or groups, represented by the name of measures of position.

This type of frequency has been replaced by one or more updated functions that may provide better precision and better use of their names. Although the compatibility in previous versions is still present, currently the usefulness of the new functions must be taken into account, since in the future they may not be available in Excel versions.

Index

## Quartile functions

These values have the ability to divide any given data sample into four equal parts. Using it can quickly assess the spread and central tendency of a data set, which are very important initial steps to allow a better understanding of the data.

Its function has been replaced by one or more updated functions that manage to provide greater precision where names can be more clearly reflected when used.

This important function is still available for compatibility in earlier versions of Excel.

In your computation with continuous variable distributions such as cluster data, you can easily make the parts into which the distribution is to be divided to be completely equal. Despite this, in direct variable distributions such as isolated data, we have to resign ourselves to the fact that the parts are relatively equal.

Unfortunately, there is no way of knowing how this approach can be carried out, although there are many different methods in the scientific literature, which lead to different results. Therefore, when calculating any ungrouped data set using software, calculators, or manually, it is necessary to know and indicate the method that has been used.

They are values that divide a data table into four groups that have relatively the same number of observations. In total it has 100%, divided into four equal parts: 25%, 50%, 75% and 100%.

### First quartile Q1

- 25% of the data is less than or equal to this value.

### Second quartile Q2

- It is the median, that is, 50% of the data is also less than or equal to this value.

### Third quartile Q3

- It has 75% of the data, which in the same way is less than or equal to the value.

### Interquartile range

It is the distance between the first quartile and the third, which allows it to cover the central 50% of the data.

These position measures are computational values and not data observations. Therefore, its function is to interpolate between two observations in order to calculate the data accurately.

Given that the median and interquartile range are not affected by extreme observations, a better central measure can be constituted and in the same way the dispersion of the asymmetric data sets, compared to the mean and standard deviation.

## What are quartiles for in statistics?

When it comes to descriptive statistics, measures of position that are not central give the opportunity to know other characteristic points of the distribution that are not the probabilities of the central values.

The quartiles can order from least to greatest and divide this distribution of values into four parts, in such a way that each of them will have the same number of frequency numbers.

## How are quartiles used in Excel?

When data is set up and varies sharply, a number of methods must be applied to help determine the values. Previous versions of Excel used methods where they used the middle of the data set to find the median of that subset of data.

With this method several unusual results can be achieved, this gave an impetus to make some changes in the Excel methodology, resulting in the exclusion of the middle quartile and thus better results were achieved. Since then, Excel 2010 continues to be the most original and the most used today.

To use it, follow the steps that we will explain below:

**To begin you must**open a new Microsoft Excel 2010 spreadsheet and click on the cell at the top of the spreadsheet.

**Once the spreadsheet is open**, filled with the data set in the first column of cells, it is important to place each number in its own cell.

**It will click on cell B1**, then type = tri to open the pop-up menu with three options. Double click on Quartile exc, with this you will be able to use the new most updated version of the quartile function.

**Double click on the Quatile.inc part**, in this part you will use the most outdated version of the function. In case you need this sheet to work with previous versions of Excel, you just have to double click on the quartile function.

**You should know that Quatile.inc and quartile**are totally the same, but quartile only works with the outdated version of Excel.

**Once you’ve made your choice**, Excel will fill in the name of the function and place an open parenthesis in the formula bar.

**Click on cell A1**and hold down the mouse button and drag it to the entry at the end of the data in the column and there you will be able to release the button. Press the key where the comma is.

**Write down the 1, 2 or 3 in the formula bar**. The number 1 will give you the first quartile, the number 2 will be the second quartile, which at the same time will be the median, and the number 3 will give you the third quartile.

**If you are using the Quartile.inc function**, you can also enter the number 0 or 4, with this you can achieve the minimum value and the maximum value individually.**To close**, type a parenthesis and hit the enter key. With this, the formula will disappear and will be replaced by the desired quartile for the data set. The number that appears is the one that will represent the value into which the range of numbers is divided into quarters.

## Example with results of the quartiles

The height in centimeters of the participants of a baseball team will be calculated, this is: 175, 168, 171, 178, 176, 174, 165, 169, 170, 172, 172, 167, 166, 170, 165, 177.

Check:

- What is the stature that leaves 25% under yes?
- Between what height is 75% of the data series?

### Answer to question number 1

** Step 1** : The data will be ordered from smallest to largest:

165, 165, 166, 167, 168, 169, 170, 170, 171, 172, 172, 174, 175, 176, 177, 178, 181.

** Step 2** : the position of Q1 will be calculated, which represents 25% of the data series:

Q1= k (N/4) = 1 (17/4) = 1 (4.25)= 4.25

When checking position 4, it corresponds to the height of 167 centimeters, but since there are decimals, it has to be interpolated between position 4 and 5 as follows:

Q1= 167 + 0.25 (168-167) = 167 + 0.25 (1) = 167 + 0.25 = 167.25

** Step 3** : The value of Q1 is 167.25 centimeters and below it, it leaves 25% of the data series.

### Answer to question number 2

** Step 1** : The data will be ordered from smallest to largest.

165, 165, 166, 167, 168, 169, 170, 170, 171, 172, 172, 174, 175, 176, 177, 178, 181.

** Step 2** : The position of Q3 representing 75% of the data series will be calculated:

Q3 = k (N / 4) = 3 (17/4) = 3 (4.25) = 12.75

When the position 12 is revised, it corresponds to the height of 174 centimeters, but since there is the presence of decimals, the position 12 and 13 must be interpolated as follows:

Q3= 174 + 0.75 (175-174) = 167 + 0.75 (1) = 174 + 0.75 = 174.75

** Step 3** : The value of Q3 is 174.75 centimeters, which means that between the values 165 and 174.75 centimeters there is 75% of the data series.

## Conclusion of the use of quartiles

To conclude, it can be said that quartiles are measures of location, whose function is to inform the value of some variables that occupy a position of our interest, which are directly related to the distribution of a number of numbers of parts, where each one of them has the same value of said variables.

It is one of the three points that order a group of numerical data into four equal parts. These points are called the lower, middle and upper quartiles, which are used to generate an idea of the dispersion of certain data sets.

Dr. Samantha Robson ( CRN: 0510146-5) is a nutritionist and website content reviewer related to her area of expertise. With a postgraduate degree in Nutrition from The University of Arizona, she is a specialist in Sports Nutrition from Oxford University and is also a member of the International Society of Sports Nutrition.