partitional values1

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