# Statistics - Deciles Statistics

A system of dividing the given random distribution of the data or values in a series into ten groups of similar frequency is known as deciles.

## Formula

${D_i = l + \frac{h}{f}(\frac{iN}{10} - c); i = 1,2,3...,9}$

Where −

• ${l}$ = lower boundry of deciles group.

• ${h}$ = width of deciles group.

• ${f}$ = frequency of deciles group.

• ${N}$ = total number of observations.

• ${c}$ = comulative frequency preceding deciles group.

### Example

Problem Statement:

Calculate the deciles of the distribution for the following table:

fiFi
[50-60]88
[60-60]1018
[70-60]1634
[80-60]1448
[90-60]1058
[100-60]563
[110-60]265
65

Solution:

#### Calculation of First Decile

${\frac{65 \times 1}{10} = 6.5 \\[7pt] \, D_1= 50 + \frac{6.5 - 0}{8} \times 10 , \\[7pt] \, = 58.12}$

#### Calculation of Second Decile

${\frac{65 \times 2}{10} = 13 \\[7pt] \, D_2= 60 + \frac{13 - 8}{10} \times 10 , \\[7pt] \, = 65}$

#### Calculation of Third Decile

${\frac{65 \times 3}{10} = 19.5 \\[7pt] \, D_3= 70 + \frac{19.5 - 18}{16} \times 10 , \\[7pt] \, = 70.94}$

#### Calculation of Fourth Decile

${\frac{65 \times 4}{10} = 26 \\[7pt] \, D_4= 70 + \frac{26 - 18}{16} \times 10 , \\[7pt] \, = 75}$

#### Calculation of Fifth Decile

${\frac{65 \times 5}{10} = 32.5 \\[7pt] \, D_5= 70 + \frac{32.5 - 18}{16} \times 10 , \\[7pt] \, = 79.06}$

#### Calculation of Sixth Decile

${\frac{65 \times 6}{10} = 39 \\[7pt] \, D_6= 70 + \frac{39 - 34}{14} \times 10 , \\[7pt] \, = 83.57}$

#### Calculation of Seventh Decile

${\frac{65 \times 7}{10} = 45.5 \\[7pt] \, D_7= 80 + \frac{45.5 - 34}{14} \times 10 , \\[7pt] \, = 88.21}$

#### Calculation of Eighth Decile

${\frac{65 \times 8}{10} = 52 \\[7pt] \, D_8= 90 + \frac{52 - 48}{10} \times 10 , \\[7pt] \, = 94}$

#### Calculation of Nineth Decile

${\frac{65 \times 9}{10} = 58.5 \\[7pt] \, D_9= 100 + \frac{58.5 - 58}{5} \times 10 , \\[7pt] \, = 101}$