Table of Contents

Statistics – Deciles Statistics

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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 −

Problem Statement:

Calculate the deciles of the distribution for the following table:

Solution:

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

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

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

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

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

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

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

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

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

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