partitional values1
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Partition values
Chapter 2
Partition values
Partition values are the values of a series which divide the data into a number of equal parts.
Median, quartiles, deciles , Percentiles etc. are the important partition values.
Quartiles
Quartiles are those values of the variable, which divide the data into 4 equal parts.
Thus there are three quartiles known as Q1, Q2 and Q3.
25% of items of a have values less than Q1.For Q3 ,75 % of the items have values less than Q3.
QuartilesSplit Ordered Data into 4 Quarters
Position of i-th Quartile
and are Measures of Non central Location = Median, a Measure of Central Tendency
25% 25% 25% 25%
( )1Q ( )2Q ( )3Q
Data in Ordered Array: 11 12 13 16 16 17 18 21 22 ( ) ( )
1 1
1 9 1 12 13Position of 2.5 12.5
4 2Q Q
+ += = = =
1Q 3Q
2Q
( ) ( )1
4i
i nQ
+=
Deciles
Deciles are those values of the variable, which divide the data into 10 equal parts.
Thus there are nine quartiles known as D1,D2,…D9.
20% of items of a have values less than D2. 40 % of the items have values less than D4
Percentiles
Percentiles are those values of the variable, which divide the data into 100 equal parts.
Thus there are ninety nine quartiles known as P1,P2,….P100
20% of items of a have values less than P20.40 % of the items have values less than P40
Uses of quartiles
Helps to find measures of dispersion(Quartile Deviation)Coefficient of dispersion(Coefficient of
Quartile deviation)Measures of skewness (coefft of Bowley’s
coefficient skewness)
Partition values in Individual series
Write the values in ascending order of their magnitude
Then find
Median = Size of (n+1)/2 th itemQ1= size of (n+1)/4 th item
Q3 = size of 3(n+1)/4 th item
kth decile= Dk = size of th item
rth Percentile =Pr =size of th item
Question no 1
Compute the quartiles and median from the following data
33,37,30,47,60,87,15,30,45,43,44
Question no 2
Compute the quartiles for the following values
28,30,13,15,14,34,50,90,15,21
Question no 3
Compute the 6th decile and 40th percentile of the following series
52,89,101,23,95,43,55,15,65
Partition values in Discrete series
Find the Cumulative frequenciesThen findMedian = Size of (n+1)/2 th itemQ1= size of (n+1)/4 th item
Q3 = size of 3(n+1)/4 th item
kth decile= Dk = size of th item
rth Percentile =Pr =size of th item
Question no 1Find the median and quartiles from the
following data Size 4 6 10 12 18 20 25 F 3 7 10 15 8 6 4
Q1=10 Q3=18 Q2=1
Question no 2
Find Quartiles and 9th deciles and 30th percentileSize 4 6 10 12 18 20 25Freq 3 7 10 15 8 6 4
Partition values in Continuous series
1.Find the cumulative frequency
Median = Size of (N/2) th item THEN YOU WILL GET THE CLASS IN WHICH MEDIAN IS THERE
Q1= size of (N/4) th item
Q3 = size of ( 3N/4) thDk= size of (kN/10) th item where k=1,2,…9
Pr = size of ( rN/100) th item where r = 1,2,3,….99
Where N=∑fitemUse the interpolation formula
Where j=1,2,3For finding Q1 , FIRST FIND THE N/4 TH VALUE THEN APPLY THE FORMULA ACCRDINGLY
Question no 1
Find D7 and P90 for the data given below Age 0-10 10-20 20-30 30-40 40-50 50-60 No of person 15 30 53 75 100 110
60-70 70-80 115 125
Home work 1
Compute the 80th percentile for the following values
28,30,13,15,14,34,50,90,15,21
Home work 2
Obtain the Quartiles for the data given below Age 0-10 10-20 20-30 30-40 40-50 50-60 No of person 15 30 53 75 100 110
60-70 70-80 115 125
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