## Deciles for grouped data calculator

Use Decile calculator to find the Deciles for grouped (frequency distribution) data.

Deciles Calculator (Grouped Data) | |
---|---|

Type of Freq. Dist. | DiscreteContinuous |

Enter the Classes for X (Separated by comma,) | |

Enter the frequencies (f) (Separated by comma,) | |

Which Octile? (Between 1 to 9) | |

Results | |

Number of Obs. (N): | |

Required Decile : D{{index}} | |

## Deciles for grouped data formula

Deciles are the values of arranged data which divide whole data into **ten** equal parts. They are 9 in numbers namely $D_1,D_2, \cdots, D_9$. Here $D_1$ is first decile, $D_2$ is second decile, $D_3$ is third decile and so on.

## Formula

For discrete frequency distribution, the formula for $i^{th}$ decile is

`$D_i =\bigg(\dfrac{i(N)}{10}\bigg)^{th}$ value, $i=1,2,\cdots, 9$`

where,

- $N$ is total number of observations.

For continuous frequency distribution, the formula for $i^{th}$ quartile is

`$ D_i=l + \bigg(\dfrac{\dfrac{iN}{10} - F_<}{f}\bigg)\times h $`

; `$i=1,2,\cdots, 9$`

where,

- $l$ is the lower limit of the $i^{th}$ decile class
- $N=\sum f$ total number of observations
- $f$ frequency of the $i^{th}$ decile class
- $F_<$ cumulative frequency of the class previous to $i^{th}$ decile class
- $h$ is the class width

## Decile for grouped data example

A librarian keeps the records about the amount of time spent (in minutes) in a library by college students. Data is as follows:

Time spent | 30 | 32 | 35 | 38 | 40 |
---|---|---|---|---|---|

No. of students | 8 | 12 | 20 | 10 | 5 |

Calculate $D_1$ and $D_6$.

### Solution

$x_i$ | $f_i$ | $cf$ | |
---|---|---|---|

30 | 8 | 8 | |

32 | 12 | 20 | |

35 | 20 | 40 | |

38 | 10 | 50 | |

40 | 5 | 55 | |

Total | 55 |

**Deciles**

The formula for $i^{th}$ deciles is

$D_i =\bigg(\dfrac{i(N)}{4}\bigg)^{th}$ value, $i=1,2,\cdots, 9$

where $N$ is the total number of observations.

**First Decile $D_1$**

`$$ \begin{aligned} D_{1} &=\bigg(\dfrac{1(N)}{10}\bigg)^{th}\text{ value}\\ &= \bigg(\dfrac{1(55)}{10}\bigg)^{th}\text{ value}\\ &=\big(5.5\big)^{th}\text{ value} \end{aligned} $$`

The cumulative frequency just greater than or equal to $5.5$ is $8$. The corresponding value of $X$ is the $1^{st}$ decile. That is, $D_1 =30$ minutes.

Thus, $10$ % of the students spent less than or equal to $30$ minutes.

**Sixth Decile $D_6$**

`$$ \begin{aligned} D_{6} &=\bigg(\dfrac{6(N)}{10}\bigg)^{th}\text{ value}\\ &= \bigg(\dfrac{6(55)}{10}\bigg)^{th}\text{ value}\\ &=\big(33\big)^{th}\text{ value} \end{aligned} $$`

The cumulative frequency just greater than or equal to $33$ is $40$. The corresponding value of $X$ is the $6^{th}$ decile. That is, $D_6 =35$ minutes.

Thus, $60$ % of the students spent less than or equal to $35$ minutes.

Hope you like **Decile for grouped data calculator** and step by step explaination with example. Click on Theory to read more about decile for group data.