Quartile, Decile and Percentile

If a data set is arranged in ascending or descending order of magnitude, then the median divides the data set into two equal parts.

Cumulative frequency is the frequency of a random variable below a particular level. It tells how often the value of the random variable is less than or equal to a particular reference value.


Quartiles are the values (of observations) that divide the data set into four equal parts called quarters.

Q1 represents the lower or first quartile.

Q2 represents the middle or second quartile. It is same as median.

Q3 represents the upper or third quartile.


The nine values which divide the data set into ten equal parts are called deciles, denoted by D1, D2, D3…D9.


The 99 values which divide the data into 100 equal parts are called percentiles. They are denoted as P1, P2, …..P99.


In a grouped frequency distribution:


Quartile = L + c × [(n/4) – C]/f

Decile = L + c × [(n/10) – C]/f

Percentile = L + c × [(n/100) – C]/f


Where,

L = lower boundary of class where n/4th value lies

C = cumulative frequency of class previous to this class

f = frequency of class in which n/4th value lies

c = width of class in which n/4th value lies








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  • Q1

    Take the number of plants in different houses and find seventh decile number of plants per house.

    Marks:3
    Answer:

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  • Q2

    What is the general formula for percentiles for ungrouped data?

    Marks:1
    Answer:

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  • Q3

    What is the general formula for deciles for ungrouped data?

    Marks:1
    Answer:

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  • Q4

    What is the general formula for quartiles for ungrouped data?

    Marks:1
    Answer:

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  • Q5

    The marks of 9 students in a test were 15, 17, 29, 2, 2, 3, 16, 14 and 12.Find the third decile?

    Marks:2
    Answer:

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