Partitional Values1
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    Partitional Values1 Partitional Values1 Presentation 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