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.

 

image

 

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:

image

 

image

 

image

 

Second Quartile Q2

 

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

 

image

 

image

 

Fifth Decile D5

 

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

 

image

 

image

 

50th Percentile P50

 

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

 

image

 

image

 

Median of Frequency Distribution

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

 

image

 

image

 

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.

36 responses to Quartiles, Deciles and Percentiles (Grouped Data)

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. ^^

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…

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.

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

Leave a Reply