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 −

  • ${l}$ = 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}$


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