Partition Values || Describing Data: Summary Measures || Bcis Notes

Partition Values

Partition values are those varied values that divide the total set of observations into four equal parts maybe 4, 10 or 100.

Partition values or fractiles such a quartile, a decile, etc. are the different sides of the same story. In other words, these are values that divide the same set of observations in different ways.

1. Quartiles

Quartiles are those varied values that divide the total set of observations into four equal parts. So, they are 3-quartiles. They are denoted by Q1, Q2 & Q3. such that Q1 < Q2 <Q3.

2. Deciles

Deciles are those varied values which the total sets of observations into 10 equal parts. So, there are 9-deciles. They are denoted by D1, D2, …, D3 such that D1 < D2 < … < D9.

3. Percentiles

Percentiles are those varied values that divide the total set of observations into 100 equal parts. So, there are 99-percentiles. They are denoted by P1, P2, …, P99.

Computation of partition values

The procedure for calculating the quartiles, deciles, and percentiles in case of individual series, discrete series and continuous series is same as a median.

Individual Series,

Here, i=1, 2, 3

Here, i=1, 2, …, 9

Here, i=1, 2, …, 99

 

Discrete Series,

 

Here, i=1, 2, 3

Here, i=1, 2, …, 9

Here, i=1, 2, …, 99

 

Continuous Series,

Here, i=1, 2, 3

Here, i=1, 2, …, 9

Here, i=1 ,2 ,…, 99

where,

l=lower limit of the median class

i=Number of quartile

N=Number of Observations

f=frequency of the median class

c.f.=c.f. of preceding the median class

h=size of the median class

 

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