# Partition Values

## Introduction: Partition Value

Partition values are used to divide the total number of observations of a statistical series into equal parts. It is essential to understand that in order to use partition values, we must sort data either in ascending or descending order. Commonly used partition values include quartiles, deciles, and percentiles.

As the names suggest, quartiles divide the observations into four equal parts, deciles divide into ten equal parts while percentiles divide data into hundred equal parts. It is important sometimes to divide data to see the effects of distribution in a statistical series. This leads to better observation and grouping of data sets and probability distributions.

## What are Quartiles?

Quartiles are nothing else but three values that divide the sorted data into four equal parts

• The first quartile or Q1 is also known as the lower quartile. It is the number halfway between the first (lowest) number and the middle number.

• The second quartile Q2 is also known as the median. It is the number halfway between the lowest number and the highest number in the statistical series.

• The third quartile or Q3 is the number halfway between the middle number and the highest or last number in the statistical series.

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In the series above 3 is the first quartile or Q1. 6 is the second quartiles or Q2 (median), and 9 is the third quartile.

Quartiles summarize the central variability and tendency of a dataset or distribution. They are a set of descriptive statistics.

Quartiles can also be termed as a type of percentile. A percentile shows a value with a certain percentage of the data falling under it.

In general terms, n% of the data falls below the nth percentile.

• The first quartile is the lowest quartile. It is the 25th percentile, meaning that 25% of the data falls below the first quartile.

• The second quartile is the median. It is in the 50th percentile, meaning that 50% of the data falls below it.

• The third quartile is the upper quartile which is the 75th percentile, meaning that 75% of the data falls below it.

By splitting the data at the 25th, 50th, and 75th percentiles, we can divide the data into four equal parts. In a sample or dataset, the quartiles are used to divide the data into four groups with the same number of observations. In a probability distribution, the quartiles set the distribution’s range into four equal intervals with the same probability.

As quartiles divide a distribution into four equal parts, deciles divide a distribution into ten equal parts. While dividing data into deciles, a decile rank or number is assigned to each data point in order to evenly sort the data into descending or ascending order.

In other words, a decile has 10 categorical steps while a quartile has four and a percentile has 100.

The concept of a decile is widely used in finance and economics to analyze data sets. It is often used to check the performance of a portfolio of investments in finance.

Decile, percentile, quartile, and quintile are various types of quantiles that are used in statistics. A quantile is a value that divides the given observations in a sample into some equal subsections. In practice, there will always be one lesser quantile than the total number of subsections created. In the case of deciles, the number of quantiles is therefore

## What is Decile?

We can state that a decile is a type of quantile that divides a dataset into 10 equal subsections by having 9 data points in the data set. Each subsection will represent 1/10 of the original sample or the population. Decile is used to order given large amounts of data in an increasing or decreasing order.

This ordering is usually done by using a scale from 1 to 10 where each next value shows an increase by 10 percentage points.

Decile Class Rank

Decile rank, also known as decile class rank, is used to split the given data and order it according to some specified metric. Once the given data is sorted into deciles then each subsequent data set is given a decile rank. Each successive rank has an increase by 10 percentage points and they are used to order the deciles in the increasing order. The 5th decile of distribution is the median of the statistical series.

## How to calculate decile?

The simple calculation of decile can be made with the following formulas:

• D1 or the first decile = Value of (n+1)/10th data

• D2 or the second decile = Value of 2 (n+1)/10}th data

• D3 or the third decile = Value of 3 {(n+1)/10}th data

• D4 or the fourth decile = Value of 4 {(n+1)/10}th data

• D9 or the ninth decile = value of 9 {(n+1)/10}th data

## What is a Percentile?

A percentile (or a centile) is a tactic used in statistics to indicate the value below which a specific percentage of observations in a group of distributions or observations fall.

For example, the 30th percentile is the value (or score) under which 30% of the observations can be found.

Percentile and percentile rank are terms often used in the reporting of scores from norm-referenced tests.

Percentile and percentile rank are terms often used in the reporting of scores from norm-referenced tests.

For Example, when a score is at the 85th percentile, where 85 is the percentile rank, it is equal to a value under which 86% of the observations will be found. In contrast, if it is in the 86th percentile, the score will be at or below the value of which 85% of the observations can be found. Every score in this case is in the 100th percentile.

The 25th percentile can therefore be called the first quartile (Q1), the 50th percentile is the median or second quartile (Q2), and the 75th percentile is the third quartile (Q3). As mentioned before, percentiles and quartiles are specific types of quantiles.

The range of values that have the central half of the observations is known as the interquartile range: this means, the range between the 25th and 75th percentiles (the range including the values that are 25% above or 25% below the median).

Percentile is used with the data set’s median value to report the data that are usually non-normally distributed.

## Conclusion

Quantiles are a great way to divide data sets into sensible series. It may be sometimes hard to get references for a study from given data until the data set is divided into quantiles. That is why there is a widespread use of quantiles in statistics and economics. They are a favorite tool to group the observations so that data can be used more specifically in statistical calculations.

## FAQs

Q1. What are the three types of quantiles?

Ans. The three types of quantiles are quartiles, deciles, and percentiles.

Q2. Which is the largest quantile and how many parts are there in it?

Ans. The percentile is the largest quantile that has 100 equal parts in it.

Q3. Why are data sets divided into quantiles?

Ans. It may sometimes be hard to evaluate and infer the values and importance of data from a large data set that is not systematically arranged. Partition values or dividing the data sets into quantiles help statisticians get references easily. That is why data sets are grouped into quantiles.

Updated on: 13-Oct-2022

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