# Quartiles, Deciles and Percentiles for Ungrouped Data

When data is arranged in ascending or descending order, it can be divided into various parts by different values such as quartiles, deciles and percentiles. These values are collectively called quantiles and are the extension of median formula which divides data into two equal parts. Since the basic purpose of these partition values is to divide data into different parts therefore a relationship exists between them. This relationship is given below and is elaborated with the help of simple problem.

Problem: Following are the number of defective items produced in a month by a machine for the last 24 months. 45, 30, 36, 26, 16, 21 33, 40, 32, 14, 10, 29, 23, 39, 17, 11, 18, 34, 19, 24, 21, 35, 42, 37

Prove that Second Quartile= Fifth Decile = 50th Percentile = Median

Solution:

Arrange data in ascending order:
10, 11, 14, 16, 17, 18, 19, 21, 21, 23, 24, 26, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 42, 45

### Second Quartile Q2

Since the data given in the problem is ungrouped therefore following formula will be used for the calculation of second quartile.

### 5th Decile

The calculation of 5th decile for ungrouped data is given below:

### 50th Percentile (P50)

The calculation of 50th percentile for ungrouped data is given below:

### Median

If the observations are Even in numbers, then median is the arithmetic mean of two central values. These two central values are calculated as:

Hence it is proved that:

Second Quartile= Fifth Decile = 50th Percentile = Median = 27.50

In order to see the relationship between Quartiles, Deciles and Percentiles in case of frequency distribution click here.

### 52 responses to Quartiles, Deciles and Percentiles for Ungrouped Data

jeffrey says:

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jeffrey says:

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mbalectures says:

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ankur says:

great page. lucid explanations thanks

Sovannarith Lim says:

It help me a lots, thanks.

Yoly says:

How do you compute foe first decile and first percentile?

Asifo says:

@Yoly, Just replace the 5 by 1 in both formula for decile and percentile.

For decile, i = 1, 2, 3, 4, 5, 6, 7, 8, 9
For percentile i = 1, 2, 3, . . . . . . . 99
For Quartile i = 1, 2, 3

also mention here for even no. of integers in ungrouped data

computation of decile for grouped data.. please.. 😀

ahvick says:

its good………..

how i can calculate P99(percentile99) with ungroup data

almas says:

can u find percentile p99 with ungrouped

tnk-u so much 4 ds website….8 helps me a lot. 8 makes me knowledgeable in terms of statistic subject..

JESSE says:

thnx alot 4 dis…its realy helped me

thank you so much for giving the formulas of quartile, decile and percentile i was looking all over the web but no one was giving this much clearly the formulas with example so once again thank you so much

zebedayo sifael says:

great idea….congratulation sir

Riliz kandoliya says:

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em getting too much inspire 🙂 ….. thanks aloottt

it is suffiecient explation for this topic

Rupesh says:

i helped me to understand the concepts

Rupesh says:

it helped me to understand the concepts

Abubakar says:

I really appriciate your information. Tanks

fairuzahmahmood@gmail.com says:

Why is it some formula for percentile just use n not n+1 ?. What is the difference?

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M.Umer Shaikh says:

gud, useful material for statistical students.

natnat2 says:

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blackering boob says:

way lain???? panget

bubu says:

gr8

Kelash Kumar says:

Thanks alot 🙂

Tewachew says:

thanks so much it is realy helped me

pamabu says:

good illustration

thanks a lot!

examples of solving the percentile, decile and quartile of grouped data…..please!

nelson ochieng says:

This is just so wonderful..i couldn’t understand what my lecturer was explaining until i got it here..Am in kenya!

Thanks :))))))))

nura fernandez says:

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KWIZERA POLLY says:

What is the first percentile of the data below,23,45,67,23,56,34,54,76,71,43

lucs says:

what is n in the formula? sir

how about if the upper quartile is 7.75th term.

Alli says:

Very good

Julie says:

Where did you get 0.5 in finding Q2??

Julie says:

Where did you get 0.5 in finding Q2??

novem ,matuguinas says:

how to solve this decile for ungroup data?

anthony is a secretary in one big company in metro manila.his salary is in the 7th decile.should anthony be glad about his salary or not? explain your answer?

solution: 70% of the employeed received a salary that is less than or equal to his salaryu and 30% of the employees receive a salary that is greater than his salary.Anthony should beplease with his salary.