This Decile Calculator is a useful tool for calculating the deciles (**1**^{st} to 10^{th}) of any ungrouped (or raw) data. Our calculator provides an easy and efficient way to calculate deciles while reducing the possibility of errors.

Moreover, this calculator also calculates essential statistical measures such as the Minimum value, Maximum value, Mean, Range, and Sum of the data set.

## What is Decile in the Statistics?

In statistics, a decile is any nine values that divide a sorted dataset into **10 **equal parts with each part representing **10%** of the data’s distribution.

## Decile Formula for Raw Data

The formula to calculate the **k**^{th} decile for raw data is:

Where,

**n** is the total number of observations in the dataset**k **ranges from 1 to 9 for each respective decile.

## How to Calculate Decile?

Let us consider some examples to learn how to find a decile.

**Example 1:**

Find the **3**^{rd} Deciles of the following dataset:

48, 9, 18, 21, 15, 12, 17, 81, 78, 5

**Solution:**

**Step 1:** Arrange the data from the smallest to largest values.

5, 9, 12, 15, 17, 18, 21, 48, 78, 81

**Step 2: **Count the total number of observations in the dataset and denote it as **n**.

n = 10

**Step 3: **Use the Decile formula to calculate **D**_{3}.

**For 3**^{rd} Decile:

K = 3

n = 10

∴ K^{th} decile = [{k (n + 1)} / 10]^{th} data

3^{rd} decile = [{3 (10 + 1)} / 10]^{th} data

= [{3 (11)} / 10]^{th} data

= [33 / 10]^{th }data

3^{rd} decile = [3.3]^{th} data

**Step 4:** Separate the Integer and Fractional Parts of the obtained values of step 3.

3^{rd} decile = 3^{th} + 0.3^{th} data

**Step 5:** For “(0.3)^{th} data” subtract 3^{rd} term from the 4^{th} term, and then multiply it by “(0.3)”

3^{rd} decile = 3^{th} + [0.3 × (4^{th} – 3^{th})]

**Step 6:** Substitute the values of terms from the sorted data set.

3^{rd} decile = 12 + [0.3 × (15 − 12)]

= 12 + [0.3 × (3)]

= 12 + (0.9)

**3**^{rd} decile = 12.9

Thus, 3^{rd} decile is 12.9

**Example 2:**

Calculate **D**_{8 }of the data set: 68, 51, 28, 5, 41, 29, 19, 4, 14, 34

**Solution:**

**Step 1:** Sort the given data set in ascending order.

4, 5, 14, 19, 28, 29, 34, 41, 51, 68

**Step 2: **Identify Total Observations (n).

n = 10

**Step 3: **Use the Decile formula to calculate D_{8}.

**For 8**^{th} Decile:

K = 8

n = 10

∴ K^{th} decile = [{k (n + 1)} / 10]^{th} data

8^{th} decile = [{8 (10 + 1)} / 10]^{th} data

= [{8 (11)} / 10]^{th} data

= [88 / 10]^{th }data

= [8.8]^{th} data

8^{th} decile = 8^{th} + 0.8^{th} data

**Step 4:** For “(0.8)^{th} data” subtract 8^{th} term from the 9^{th} term, and then multiply it by “(0.8)”

8^{th} decile = 8^{th} + [0.8 × (9^{th} – 8^{th})]

**Step 4:** Substitute the values of terms from the sorted data set.

8^{th} decile = 41 + [0.8 × (51 − 41)]

= 41 + [0.3 × (10)]

= 41 + (8)

**8**^{th} decile = 49

Therefore, the 8^{th} decile is 49