# 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.

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

allison parel says:

thank you for this info. this will help me on my midterm exam for quantitative methods tomorrow.

Sovannarith Lim says:

thank a lots for this information. It can help me know clearly about Measures of Central Tendency for my final exam.

venice says:

the answer 4 inside the parenthesis isn’t multiplied to the fraction outside. anyway, they’re still the same if it’ll be multiplied to 4. ^^

Tohero says:

9c job

Desalegn says:

It is the best explanation!

James says:

Hey….thank you guys.i have been struggling to find this infomation

blessing says:

gosh;am so happy,i can’t believe that its this easy,am so happy.

peace says:

awesome,,, i dnt study stats frm books anymore 🙂

Charles says:

What an explanation!!! Thanks a lot Admin.

Nice wrk,gav me alot of option in solving my stat problems

krishna says:

thank you very much! you’re a lifesaver 😀

sameen says:

awesome!!!!!

Engineer snake says:

great job dude keep it coming!!!

ben says:

thanks , this information is very helpful

Jonlen DeSa says:

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Thanks a lot!! I got a final paper in 5 hours..

angel parmar says:

how to calculate percentile 46 means p46?

very impressive way of explanation, best comparasion. so nice of u people…

Hassan says:

excellent !

yinkaar says:

Thank so much I really appreciate ur generosity

justice knight says:

u guyz r wwwooow, it has really worked 4 me, nd m not sure m gonna fail dis exam in Jesus’s name. if u agree wif me jus say, Amen…

IU's says:

Thanks for sharing such valuable data…

Richard Silavwe says:

Hey! you are such an asset to the society. Keep up the good work.you have made the subject to look very simple but detailed.

JOYJOY says:

great job. but i just have a question, how did you come to a conclusion that 10th value is in interval, 13.5-16.5? thanks.

FRIDAH KENDI says:

Very good explanations.
I didnt get, how do i calculate the Quartile frequency as in how many elements are in Q1,Q2,Q3,Q4 to add up to N.

Bryan says:

Thanks for this. This will help me to reduce the size of my report by grouping the sample size.

Shampy says:

Thanks Bro .. it really helped me …. :*

Iqra says:

AWESOME 🙂
Thanks

What a mavelous explanation guys.you guys KEEP IT UP

Marissa Baker says:

Thank you for sharing your knowledge! You really help me

cosyz says:

thanks alot

thanks.

eyasu leta says:

thank you

BeauIsMe says:

Hey how do you say that 13.5 – 26.5 is in the 10th value? Please tell me T.T

Minister says:

Thank u so much, am grateful for your supply

Jay wang says:

some great work, awesomely helpful. Keep up the great work…………….

Hudson says:

You are real lecturers, easy to understand

mhona says:

thanks for these 😀

Rosalea Mariz says:

Thank you for this information.I can more easily understood. 😀

jinial says:

kahin se v help mil jata bt fir v thanks

Nyarieko Alex says:

thx a lot

Bishop says:

Its really cool, buh I couldn’t get the logic behind the C.B and the tenth Value, I think ur formula seems a lil different 4rm mine here in Nigeria, mine is
Q3=L1+(3n/4-c.f)c
—————
Fe

Kehinde says:

Nice workings, it really helped me .

mr realist says:

u guys gave me a lot of relief .Tanks alot

Bill Bennett says:

Excellent job explaining quartiles, deciles and percentiles. You are to be commended.