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.

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

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

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

Very Nice Sir! Thanku for this information

This is so much easier to be understand

thanks alot very very useful for us

awesome …

Thank you very much

benmu wonderful explanation meant for shaping young minds to perfection

wonderful explanation meant for shaping eager minds to perfection

Thanks a lot sir. 🙂

Thankz a lot sir…..

This article helped me to understand the topic into more depth …. 🙂

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.

good work,thanks sir,

Thanks more!

Very neatly explained. Thank you.

well explained

Thanks a lot sir.

Thanks alot…Its awesome

Very good explation, thank you so much

it’s such a nice explanation. thank you

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?

Thank you so much

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.

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..

thanks alot the information has real made me one step ahead