Statistics Deciles Statistics – lesscss

By | January 1, 2019

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:

  fi Fi
[50-60] 8 8
[60-60] 10 18
[70-60] 16 34
[80-60] 14 48
[90-60] 10 58
[100-60] 5 63
[110-60] 2 65
  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}$

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