# Decile Calculator

The decile calculator helps you split a dataset into different deciles and use the decile scale to compare the data. Much like percentage, percentile and quartile, the decile rank is commonly used in descriptive statistics to divide the data into samples for easier analysis. Using the decile calculation formula, our tool divides the set of observations into 10 samples and allots the decile rank accordingly.

## What does decile mean?

The definition of a decile states that it is the set of **9 values** that splits the dataset into **10 groups**. It is similar to quartiles and percentiles. Deciles are where the data points are ordered from least to greatest and split into 10 groups with an equal range of values in each. This helps us understand what a decile means.

As a special case, if there are only **9 data points** in the set, each of the 9 values will represent the 9 deciles, and there won't be a 10^{th} group of data.

## How do I calculate decile using the decile formula?

To calculate the decile values, we need **at least 9 data points** in our dataset. We can find the solution for the decile calculation using the following decile formula:

where:

**k = 1, 2, 3, ..., 9**; and**n – Number of data points**.

So, for example, if there are **99 data points** and we want to know how to calculate **decile 1 or the 1st decile**, we'll follow these steps:

- We'd first arrange the values in
**increasing order**to find the decile rank. - Use the d1 formula or the formula for the 1st decile:

- So in the ordered dataset, we get:

This way, by using the d1 formula (1st decile formula), we see that for a set of 99 values in the decile scale, the **1st decile** will be the **10 ^{th} value**! We can also see that the 1

^{st}decile rank is equivalent to the 10

^{th}percentile rank!

## Decile calculator solution (example)

Let's say we have the following 20 values in our dataset:

45 | 8 | -9 | 10 | 31 |

81 | -6 | -40 | 0 | 9 |

77 | 54 | -43 | -2 | 10 |

31 | 0 | 9 | -9 | 5 |

First, we'd arrange them in ascending order to get this:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|

-43 | -40 | -9 | -9 | -6 | -2 | 0 | 0 | 5 | 8 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
---|---|---|---|---|---|---|---|---|---|

9 | 9 | 10 | 10 | 31 | 31 | 45 | 54 | 77 | 81 |

We can estimate the 9 deciles using the formula:

Applying this gives us the following results:

1 | 2.1 | -36.9 |
---|---|---|

2 | 4.2 | -8.4 |

3 | 6.3 | -1.4 |

4 | 8.4 | 2 |

5 | 10.5 | 8.5 |

6 | 12.6 | 9.6 |

7 | 14.7 | 24.7 |

8 | 16.8 | 42.2 |

9 | 18.9 | 74.7 |

If the decile is a fractional or a decimal value, for example, the 2.1^{th} data in the above dataset, then its calculation would be a little different, and unlike a median calculation. We would calculate the **2.1 ^{th} data point** as follows:

**2.1**is**0.1**of the distance between 2 and 3, so we will first find the difference between the 2^{nd}and 3^{rd}data points. This will give us`-9 - (-40) = 31`

.- We'd then find
**0.1**of**31**by multiplying, which would give us`0.1 × 31 = 3.1`

. **3.1**units from the 2^{nd}data point is`-40 + 3.1 = -36.9`

.- Therefore, we get the
**1**of the above example dataset as the^{st}decile**2.1**, which is^{th}data point**-36.9**!

## Common uses of decile, quartile and percentile

We work with a variety of data in our day-to-day lives and professions. Sometimes, the data that we have may follow a specific kind of distribution, such as:

Even beyond identifying the type of data distribution, we may sometimes want to rank the data on a normalized scale such as test or exam scores, and a few such ranking mechanisms that are most used are:

- Quartiles – to find the top 25% data;
- Deciles – to find the top 10% data; and
- Percentiles – to find the top 1% data.

## FAQ

### What is decile?

The decile definition states that it is a statistical measure that **divides a dataset into 10 buckets based on the decile scale**. The top decile, for instance, refers to the top (1/10)^{th} of the data values. We can find what the deciles are using the solution to the decile calculation formula. Once we calculate the 9 deciles of the dataset, we can partition the set into 10 segments or ranks.

### Is 90th percentile equivalent to top decile?

The 90^{th} percentile of a dataset is the same as the 9^{th} decile of the same set. Any values above the 90^{th} percentile or the 9^{th} decile will represent the top (1/10)^{th} of the data values. The 10^{th} decile (if it exists) represents the maximum of all the data values.

### How do we calculate quartiles, deciles and percentiles?

Quartiles, deciles, and percentiles are statistical measures used to rank a dataset into different numbers of buckets. To know how to calculate quartiles, deciles, and percentiles, we'd use slightly different formulas, but each of those accomplishes the following:

- Quartiles divide the dataset into 4 ranks;
- Deciles divide the dataset into 10 ranks; and
- Percentiles divide the dataset into 100 ranks.

### What is the tenth decile?

For datasets that have 9 values, we'd have only 9 deciles. But for other datasets that have 10 or more values, we will have 10 deciles, where the 10^{th} decile is simply **the highest number in the distribution**.