Quintiles Definition Explained Formula Calculation Examples

Quintiles Definition

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Quintiles segregate data samples into five equal parts that uncomplicate the data and help to understand the difference between ranges. Such as 0-20% of the bottom segment of the population in a given sample represents the first quintile. Similarly, 20- 40% represents the second quintile, 40-60% represents the third, 60-80% represents the fourth, and 80-100 is the fifth or upper quintile.

Key Takeaways

Quintiles segregate any given data into 20% of its sample size or population. It distributes the sample into lower and upper quintiles, while three other quintiles exist.The first or lower quintile represents the lower on-fifth segment of a data, i.e., 0-20%, while the upper one defines the upper one-fifth of the data or population, i.e., 80-100%.These are beneficial in studying large data sets or population sizes at the macro level. Thus, economists and politicians refer to such quintiles while discussing policy implications and outcomes.

Quintiles Explained

Quintiles statistics assist in segregating large data sets into smaller segments that define the various 20% of the values consistent in a data set. For instance, to understand the employment levels in 5 industries that drive the U.S. economy, an economist divides the available employment statistics into five sectors, i.e., health, technology, construction, retail and non-durable manufacturing.

This segregation helps the economist understand which industry employs the least amount of labor force, i.e., the lower fifth (0%-20%) and which employs the highest labor force, i.e., in the top quintile (80%-100%). Thus, calculating quintiles help in establishing the different cut-off point in an enormous data set such as the employment statistics, population census, and the agricultural census at the economy level.

Comparatively, the median divides a data set into two quantiles. It is a statistical tool for studying small-scale sample sizes or populations. Similarly, calculating quintiles is a way to segregate and scrutinize data into one-fifth portions from lower (0%-20%) to upper (80%-100%) segments.

Accordingly, the distribution of a data set into three segments or quartiles is known as tertiles or one-third of the population. A basic example of this is the segregation of income levels in an economy for taxation purposes – low-income, middle, and higher income.

Similarly, a quartile divides a population or a sample size into four different segments representing one-fourth or 25% of the values in the available data. Thus, dividing sample size or population into different quartiles depends on data size. Undeniably, this segregation helps governments and organizations to target and study policy implementation for particular socio-economic classes within a society.

Often large data sets concerning population are easier to study when represented in quintile statistics. Consequently, quartiles and quintiles become efficient statistical tools to understand a dataset intensively.

Formula

The formula to segregate any data into quintiles statistics is by dividing or ranking the data into five equal groups such that,

0%-20% – represents the first quintile (also known as the lower fifth)20%-40% – the second quintile40%-60% – the third quintile60%-80% – the fourth quintile80% -100% – the fifth quintile or upper quintile

To enumerate, dividing the data into equal parts in an orderly manner (ascending or descending) is similar to determining the median of any given data. Thus, after dividing the data, the next step is to find or calculate the quintile percentage as a part of the whole. Consequently, the third step involves determining the quintile range for the resultant to see how much it contributes to the whole.

For instance, income quintiles will help determine how much income people in the fourth or fifth quintile earn as their share of the total incomes generated in an economy.

Examples (with Calculation)

Let us now look at a calculation to understand the determination of quintiles statistics comprehensively,

Example #1

For example, the data below provides world over different regions’ average GDP per capita. Let us represent them with the help of quintiles statistics,

Step 1: Arrange the given data in ascending order and divide it into groups of two,

1177, 1645.5 | 2176.8, 3798.8 | 6412.4, 7696.9 | 8340.4, 13037 | 38234.1, 67514 |

Step 2: Find out the contributions of the given groups in percentages to determine the upper and lower quintiles,

Total of GDP per capita (of all given regions) = $150, 032.9Adding the average of GDP per capita of fifth group (European Union and North America) = 38, 234.1 + 67,514 = $ 105, 748.1

Thus, European Union and North America have a 70.5% share in the average GDP per capita of the given regions, i.e., these regions fall in the fourth quartile (60-80%).

Dividing the two outcomes =

Similarly,

Adding the average GDP per capita of the fourth group (Latin American and the Caribbean, East Asia, and the Pacific) = 8340.4 + 13037 = $ 21,377.4

Thus, the fourth group (Latin American, Caribbean, East Asia, and Pacific), with a share of 14.2%, falls in the lower fifth (0-20%). Moreover, in this example, the different economic quintiles represent the stark inequalities in these ten regions’ average GDP per capita.

Dividing it by total (of all given regions) =

Example #2

A teacher wishes to calculate the percentage of students falling under a particular class of quintiles as per the marks they secured and the range they fall under. Thus for a class of 60 students, the teacher aims to determine particular focus groups for extra classes,

Thus, the number of students that fall under the upper fifth (marks secured between 80-100) = 22/60 x 100 = 36.7%
In like manner, the teacher determines the lower fifth (marks secured between 0-20) = 6/60 x 100 = 10%