## What is a decile?

A decile is a quantitative method of dividing a classified data set into 10 equally sized subsections. This type of data classification is carried out in the context of many academic works and statistical studies in the finance and economy the fields. Data can be ordered from largest to smallest value, or vice versa.

A decile, which has 10 categorical compartments, can be contrasted with percentiles which have 100, quartiles which have four, or quintiles who have five.

Key points to remember

- A decile is a quantitative method of dividing a classified data set into 10 equally sized subsections.
- A decile rank ranks data from lowest to highest and is done on a scale of one to 10 where each successive number corresponds to an increase of 10 percentage points.
- This type of data classification is done in many academic and statistical studies in the fields of finance and economics.

## Understanding a decile

In descriptive statistics, a decile is used to rank large data sets from highest values to lowest values, or vice versa. Like quartile and percentile, a decile is a form of quantile that divides a set of observations into samples that are easier to analyze and measure.

While quartiles are three data points that divide an observation into four equal groups or quarters, a decile consists of nine data points that divide a data set into 10 equal parts. When an analyst or statistician classifies data and then divides it into deciles, they do so with the goal of discovering the largest and smallest values according to a given metric.

For example, dividing the set S&P 500 Index in deciles (50 companies in each decile) using Multiple P/Ethe analyst will discover the companies with the highest and lowest P/E valuations in the index.

A decile is generally used to assign decile ranks to a set of data. A decile rank ranks data from lowest to highest and is done on a scale of one to 10 where each successive number corresponds to an increase of 10 percentage points. In other words, there are nine deciles. The 1st decile, or D1, is the point that has 10% of the observations below, D2 has 20% of the observations below, D3 has 30% of the observations below, and so on.

## How to calculate a decile

There is not just one way to calculate a decile; however, it is important that you are consistent with the formula you decide to use to calculate a decile. A simple calculation of a decile is:

$$D1

=

Value

[

n

+

1

1

]

th Data

\begin{aligned} &\text{D1} = \text{Value of } \left [ \frac{ n + 1 }{ 10 } \right ] \text{th Data} \\ \end{aligned}

D1=Value [1n+1]th Data

$$D2

=

Value

[

2

×

(

n

+

1

)

1

]

th Data

\begin{aligned} &\text{D2} = \text{Value of } \left [ \frac{ 2 \times ( n + 1 ) }{ 10 } \right ] \text{th Data} \\ \end{aligned}

D2=Value [12×(n+1)]th Data

$$D3

=

Value

[

3

×

(

n

+

1

)

1

]

th Data

\begin{aligned} &\text{D3} = \text{Value of } \left [ \frac{ 3 \times ( n + 1 ) }{ 10 } \right ] \text{th Data} \\ \end{aligned}

D3=Value [13×(n+1)]th Data

$$D9

=

Value

[

9

×

(

n

+

1

)

1

]

th Data

\begin{aligned} &\text{D9} = \text{Value of } \left [ \frac{ 9 \times ( n + 1 ) }{ 10 } \right ] \text{th Data} \\ \end{aligned}

D9=Value [19×(n+1)]th Data

From this formula, it follows that the 5th decile is the median since 5(n+1)/10 is the data point that represents the midpoint of the distribution.

## Deciles in finance and economics

Deciles are used in the field of investment to assess the performance of a wallet or a group of mutual fund. The decile rank acts as a comparative number that measures an asset’s performance against similar assets.

For example, suppose an analyst evaluates the performance of a set of mutual funds over time, a mutual fund ranked five on a decile scale of one to 10 means it is within 50% superiors. By dividing mutual funds into deciles, the analyst can review the best and worst performing mutual funds for a given time period, ranked from lowest to highest average return on investment.

The government also uses deciles to determine the level of income inequality in the country, i.e. how the income is distributed. For example, if the top 20 earners in a country of 50,000 citizens are in the 10th decile and earn more than 50% of the country’s total income, it can be concluded that there is a very high degree of income inequality. income in this country. . In this case, the government can introduce measures to reduce the pay gap, such as increasing the income tax wealthy and creative property taxes to limit the share of assets that can be passed on to beneficiaries as an inheritance.

## Example of decile

The table below shows the ungrouped scores (out of 100) for 30 candidates:

48 |
52 |
55 |
57 |
58 |
60 |
61 |
64 |
65 |
66 |

69 |
72 |
73 |
75 |
76 |
78 |
81 |
82 |
84 |
87 |

88 |
90 |
91 |
92 |
93 |
94 |
95 |
96 |
97 |
99 |

Using the information presented in the table, the 1st decile can be calculated as follows:

- = Value of [(30 + 1) / 10]th data
- = Value of the 3.1st datum, i.e. 0.1 of the path between scores 55 and 57
- = 55 + 2 (0.1) = 55.2 = D1
- D1 means 10% of the data set falls below 55.2.

Let’s calculate the 3rd decile:

- D3 = Value of 3 (30 + 1) / 10
- D3 = Value of the 9.3rd position, i.e. 0.3 between the scores of 65 and 66
- So, D3 = 65 + 1 (0.3) = 65.3
- 30% of the 30 observation scores are less than 65.3.

What would we get if we calculated the 5th decile?

- D5 = Value of 5 (30 + 1) / 10
- D5 = Value of the 15.5th position, halfway between scores 76 and 78
- 50% of scores are below 77.

Also note that the 5th decile is also the median of the observation. Looking at the data set in the table, the median, which is the middle data point of a given set of numbers, can be calculated as (76 + 78) /** **2 = 77 = median = D5. At this point, half of the scores are above and below the distribution.