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# Partitional Values1

## on Feb 02, 2010

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## Partitional Values1Presentation Transcript

• 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 Q 1 , Q 2 and Q 3 .
• 25% of items of a have values less than Q 1 .For Q 3 ,75 % of the items have values less than Q 3 .
• Quartiles
• Split 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% Data in Ordered Array: 11 12 13 16 16 17 18 21 22
• Deciles
• Deciles are those values of the variable, which divide the data into 10 equal parts.
• Thus there are nine quartiles known as D 1 ,D 2 ,…D 9 .
• 20% of items of a have values less than D 2 . 40 % of the items have values less than D 4
• Percentiles
• Percentiles are those values of the variable, which divide the data into 100 equal parts.
• Thus there are ninety nine quartiles known as P 1 ,P 2 ,….P 100
• 20% of items of a have values less than P 20 .40 % of the items have values less than P 40
• 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 item
• Q 1 = size of (n+1)/4 th item
• Q 3 = size of 3(n+1)/4 th item
• k th decile= D k = size of th item
• r th 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 6 th decile and 40 th percentile of the following series
• 52,89,101,23,95,43,55,15,65
• Partition values in Discrete series
• Find the Cumulative frequencies
• Then find
• Median = Size of (n+1)/2 th item
• Q 1 = size of (n+1)/4 th item
• Q 3 = size of 3(n+1)/4 th item
• k th decile= D k = size of th item
• r th Percentile =Pr =size of th item
• Question no 1
• Find 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 9 th deciles and 30 th percentile
• Size 4 6 10 12 18 20 25
• Freq 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
• Q 1 = size of (N/4) th item
• Q 3 = size of ( 3N/4) th
• Dk= 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=  f
• item Use 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 D 7 and P 90 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 80 th 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