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}$
