MEASURES OF CENTRAL TENDENCY

MEASURES OF CENTRAL TENDENCY
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In data analysis, partition values divide a series into equal points, including Quartiles, Deciles, and Percentiles. Learn the meaning, application, and formulas for these values to analyze data effectively. Explore how Quartiles split data into quarters, Deciles divide data into tenths, and Percentiles segment data into hundredths. Understand computations for different types of series and formulas for calculating Partition Values like Quartiles, Deciles, and Percentiles.

  • Data Analysis
  • Partition Values
  • Quartiles
  • Deciles
  • Percentiles

Uploaded on Mar 01, 2025 | 0 Views


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  1. MEASURES OF CENTRAL TENDENCY

  2. PARTITION VALUES

  3. Objectives The student will be able to: * Find the meaning of Partition values. * Find the application of formulas of partition values in different series. * Students will able to make easy solutions of numerical practices of Partition Values.

  4. Partition Values Partition values are the values of a series which divide the data into a number of equal points.

  5. Some Partition Values are Median , Quartiles , Deciles , Percentiles etc.

  6. Quartile :- It is the Quarter Value of the series. Quartiles are those values of the variables , which divides 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, 75% of the items have values less than Q3.

  7. Quartiles Split ordered data into 4 Quarters. 25% 25% 25% 25% Q1 Q2 Q3

  8. Deciles :- Deciles are those values of the variable which divides the data into 10 equal parts. Thus there are nine deciles denoted by D1.D2,.........D9. 20% of items of a have values less than D2 . 40% of the items have values less than D4 D7 will have 70% observation on its left side and 30% observation on its right side.

  9. Percentile :- Percentile are those values of the variables, which divides the data into 100 equal parts. Thus their are 99 percentiles denoted by P1,P2,P26,P56........P99. 20% of items of a have values less than P20, 40% of the items have values less than P40

  10. Computation of Partition Values Individual series Discrete series Continuous series

  11. FORMULA FOR PARTITION VALUES In case of Quartile (Q) = ( N+1) 4 In Case of Deciles (D) = (N+1) 10 In case of Percentile (P) = (N+1) 100 In the same way..............

  12. FORMULA FOR PARTITION VALUES In case of 3rdQuartile (Q3) = 3( N+1) 4 In Case of 4thDeciles (D4) = 4(N+1) 10 In case of 28thPercentile (P28)= 28(N+1) 100 And so on...

  13. lets take an Example.... In Discrete series :- Find out 1st(Q1) and 3rd(Q3) quartile , 4th Deciles (D4) and 80thPercentile (P80) 2 2 3 3 4 9 5 6 7 5 MARKS 21 11 FREQUENCY Come ...lets solve it...

  14. Solution:- Compute c.f. first....... MARKS FREQUENCY C.F. 2 5 14 35 46 51 2 2 3 9 3 4 5 21 11 5 6 7

  15. Q1 = size of (N+1)item => 51+1 4 Size of 13thitem lies in the c.f. 14,whose variable is Thus , Q1 = 4 Q3= size of 3(N+1) item 4 Size of 39thitem lies in the c.f. 46,whose variable is Thus , Q3 = 6 D4= size of 4(N+1) item 10 Size of 20.8thitem lies in the c.f. 35,whose variable is 5 Thus , D4 = 5 P80= size of 80 (N+1) item 100 Size of 41.6thitem lies in the c.f. 46,whose variable is 6 Thus , P80 = 6 Size of 13thitem = 4 4 3 (51+1) 4 = 39THItem => 6 => 4 (51+1) = 20.8THItem 10 =>80 (51+1) = 41.6THItem 100

  16. Hence......you found Partition values :- Q3 = 6 Q1 = 4 P80 = 6 D4 = 5

  17. Same Way........ With the same way you can find out Partition Values in individual series as well as continuous series easily...

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