# 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

Di=l+hf(iN10−c);i=1,2,3…,9Di=l+hf(iN10−c);i=1,2,3…,9

Where −

·        ll = lower boundry of deciles group.

·        hh = width of deciles group.

·        ff = frequency of deciles group.

·        NN = total number of observations.

·        cc = comulative frequency preceding deciles group.

### Example

Problem Statement:

Calculate the deciles of the distribution for the following table:

Solution:

#### CALCULATION OF FIRST DECILE

65×110=6.5D1=50+6.5−08×10,=58.1265×110=6.5D1=50+6.5−08×10,=58.12

#### CALCULATION OF SECOND DECILE

65×210=13D2=60+13−810×10,=6565×210=13D2=60+13−810×10,=65

#### CALCULATION OF THIRD DECILE

65×310=19.5D3=70+19.5−1816×10,=70.9465×310=19.5D3=70+19.5−1816×10,=70.94

#### CALCULATION OF FOURTH DECILE

65×410=26D4=70+26−1816×10,=7565×410=26D4=70+26−1816×10,=75

#### CALCULATION OF FIFTH DECILE

65×510=32.5D5=70+32.5−1816×10,=79.0665×510=32.5D5=70+32.5−1816×10,=79.06

#### CALCULATION OF SIXTH DECILE

65×610=39D6=70+39−3414×10,=83.5765×610=39D6=70+39−3414×10,=83.57

#### CALCULATION OF SEVENTH DECILE

65×710=45.5D7=80+45.5−3414×10,=88.2165×710=45.5D7=80+45.5−3414×10,=88.21

#### CALCULATION OF EIGHTH DECILE

65×810=52D8=90+52−4810×10,=9465×810=52D8=90+52−4810×10,=94

#### CALCULATION OF NINETH DECILE

65×910=58.5D9=100+58.5−585×10,=101