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.

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

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

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. ^^

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how to calculate percentile 46 means p46?

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Thanks for sharing such valuable data…

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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.

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.

Mail me the answer

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

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

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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

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Fe

Nice workings, it really helped me .

u guys gave me a lot of relief .Tanks alot

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