# Quartiles, Deciles and Percentiles (Grouped 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 problems.

Problem: In a work study investigation, the times taken by 20 men in a firm to do a particular job were tabulated as follows:

Prove that:

### Second Quartile Q2

In case of frequency distribution, quartiles can be calculated by using the formula:

### Fifth Decile D5

In case of frequency distribution, deciles can be calculated by using the formula:

### 50th Percentile P50

In case of frequency distribution, percentiles can be calculated by using the formula:

### Median of Frequency Distribution

In case of frequency distribution median can be calculated with the help of following formula.

Hence it is proved that Q2 = D5 = P50 = Median

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

### 91 responses to Quartiles, Deciles and Percentiles (Grouped Data)

brian says:

just what i needed a present help in time of need.thnx alot

patricia says:

what about when the data is decreasing, how do we find the quartile distribution?

John Lean says:

YOUR EXPLANATION WAS GREAT! THANKS! IT HELPED ME A LOT!

eeman malik says:

Very Nice Sir! Thanku for this information

Lawrence says:

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abdullah khan says:

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aqib says:

awesome …

Abdulbari Saleh Dandashire says:

Thank you very much

bernard muiruri says:

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bernard muiruri says:

wonderful explanation meant for shaping eager minds to perfection

Paraluman says:

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Thankz a lot sir…..
This article helped me to understand the topic into more depth …. ðŸ™‚

feesat says:

thanks alot

Your explanation was clearly understandable by young learners ………thanks a lot.

Woow ….! What a nice explanation. It has halped in revising for my end of semester exam. Thanks.

Amon Joel Mwami says:

good work,thanks sir,

Atr says:

Very neatly explained. Thank you.

dzame monica says:

well explained

Thanks a lot sir.

Ali Hassan says:

Thanks alot…Its awesome

Ambrosia kibet says:

it’s such a nice explanation. thank you

chris rugu says:

how do we find the frequency given just like the value of 90th percentile to be 77.5 in a grouped data…..kindly assist how we go about such comments please?

Salman Bajwa says:

Thank you so much

Ricksss says:

I’m now reviewing for our exam and this website is really helpful for everyone especially who wants to know the exact purpose of the elements included. Nice Job?you nailed it. Thank you so much for having this. ?you’re much appreciated.

Rajath says:

Just consider if the Q1 value is 1and what should we put for c in the above formula as per your problem table
=L+h/f(1/4(N)-C)
1 is the first value of the table what should we put for the preceding value of 1 ie C..

Joseph says:

woow…what a nice explanation.thanks

Junaidu yusuf says:

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Emmanuel says:

You guys are learning shit here. It really gave me a lot off confusion, I don’t mean to discourage the readers but try other formula out and compare your answers because this is a total shit

Nazziwa Suzan says:

This is good information. Thank you very much

Malach says:

The unit is very easier
???

Malach says:

Mathematics for life

Asif says:

Its open my mind on the calculation . thanks

stephen says:

thanks a lot u have been of much help

Ibrar says:

Very easier to understand

Abdullahi Yahaya Abubakar says:

This is exactly what I need. thank you for all your effort.

Alex Talam says:

This is profound, God bless you.