Statistics - Deciles Statistics

A system of spaniding 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.

Problem Statement:

Calculate the deciles of the distribution for the following table:

Solution:

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

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

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

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

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

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

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

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

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