What is Partition Value. Give formula for calculating different Partition Values?
Ans.: Values of the items that divide the series into many parts are known as partition values. A variable may be divided into four, five, eight, ten and hundred equal parts known as Quartiles, Quintiles, Octiles, Deciles and Percentiles. The aforesaid partition values gives an idea of the formation of the series which are used in the calculation of dispersion and skewness.
Formula used for Calculating Partition Values :
|
Measures |
Individual & Discrete Series |
Continuous Series |
|
Quartiles : |
|
|
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Q1 |
Size of N + 1 th item 4 |
q1 = (N/4) th item & Q1 = l1 + i (q1 – c) f |
|
Q3 |
Size of 3 N + 1 th item 4 |
q3 = 3 (N/4) th item & Q3 = l1 + i (q3 – c) f |
|
Quintiles : Qn4 |
Size of 4 N + 1 th item 5 |
qn4 = 4 (N/5) th item & Q3 = l1 + i (qn4 – c) f |
|
Octiles : O2 |
Size of 2 N + 1 th item 8 |
o2 = 2 (N/8) th item & O2 = l1 + i (o2 – c) f |
|
Deciles : D7 |
Size of 7 N + 1 th item 10 |
d3 = 7 (N/10) th item & D3 = l1 + i (d7 – c) f |
|
Percentiles: P75 |
Size of 75 N + 1 th item 100 |
775 = 75(N/100)th item & P75 = l1 + i (p75 – c) f |
