# Calculation of Deciles for Ungrouped Data

Deciles:
The values which divide an array into ten equal parts are called deciles. The first, second, …, ninth deciles by D1, D2, …, D9 respectively. The fifth decile (D5) corresponds to median. The second, fourth, sixth and eighth deciles which collectively divide the data into five equal parts are called quintiles.

Deciles for Ungrouped Data:
Deciles for ungrouped data will be calculated from the following formulae; For Example:
We will calculate second, third and seventh deciles from the following array of data.
20 28 29 30 36 37 39 42 53 54
55 58 61 67 68 70 74 81 82 93

The data set has been arranged in ascending order from the top-left corner to the bottom-right one.
i. =4.25th item from below

The value of the 4th item is 30 and that of the 5th item is 36. Thus the second decile is a value 0.2th of the way between 30 and 36. The fifth decile will be 30+6⋅0.2=31.2. Therefore, D2=31.2.
ii. =6.3th item from below

The value of the 6th item is 37 and that of the 7th item is 39. Thus the third decile is 0.3th of the way between 37 and 39. The third decile will be 37+2(0.3)=37.6. Hence, D3= 37.6.
iii. =14.7th item from below

The value of the 14th item is 67 and that of the 15th item is 68. Thus the 7th decile is 0.7th of the way between 67 and 68, which will be as 37+0.7=67.7. Therefore, D7=67.7.
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