MEasures of Position.pptx

Powerpoint presentation

1. MREAUSE MEASURE

2. PISTOION POSITION

3. IDEVID DIVIDE

4. UQALE EQUAL

5. M E A S U R E S O F P OS I T I O N with Computer Application

6. OBJECTIVES Define measures of position Illustrate the following measures of position: – Quartiles – Deciles – Percentiles

7. NUMERICAL INFORMATION MAY BE CLASSIFIED AS: Ungrouped data Grouped data

8. MEASURES OF POSITION/QUANTILES - are techniques that divide a set of data into equal groups Fractiles are numbers that partition or divide an ordered data set into equal parts.

9. MEASURES OF POSITION/QUANTILES Used t o des c ribe th e p o sition of a d ata value in r elation to the r est o f the data. T ypes: Quartiles Percentiles Deciles

10. QUANTILES CAN BE APPLIED WHEN: Dealing with large amount of data, which includes the timely results for standardized tests in schools, etc. T r yi n g to discover the smallest as well as the largest values in a given distribution. Examining financial fields for academic as well as statistical studies.

11. M E A S U R E S O F P OS I T I O N F O R U NG R O U P E D D A T A Q U A R T I L E , D E C I L E A N D P E R C E N T I L E

12. Q U AR T I L E U N G R O U P E D DATA B Y I N S P E C T I O N

13. QUARTILE FOR UNGROUPED DATA The quartiles are the score points which divide a distribution into four equal parts.

14. Quartiles

15. Q 1 , Q 2 , Q 3 Quartiles

16. Q 1 , Q 2 , Q 3 divides ranked scores into four equal parts Quartiles

17. Q 1 , Q 2 , Q 3 divides ranked scores into four equal parts Quartiles 25% 25% 25% 25% Q 1 Q 2 Q 3

18. Q1 – LOWER QUARTILE At most, 25% of data is smaller than Q1. It divides the lower half of a data set in half.

19. Q2 – MIDDLE QUARTILE The median divides the data set in half. 50% of the data values fall below the median and 50% fall above.

20. Q3 – UPPER QUARTILE At most, 25% of data is larger than Q3. It divides the upper half of the data set in half.

21. Q1 Q2 Q3 25% 25% 25% 25%

22. Q U AR T I L E U N G R O U P E D DATA B Y M E N D E N H A L L A N D S I N C I C H M E T H O D

23. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE This method is being developed by William Mendenhall and Terry Sincich to find the position of the quartile in the given data.

24. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE Formula: Lower Quartile (L) = Position of Q1= ¼ (n+1) Q2= 2(n+1) = n+1 th observation 2 Upper Quartile (U) = Position of Q3 = ¾ (n+1) 4

25. MENDENHALL AND SINCICH METHOD : A METHOD OF FINDING THE QUARTILE VALUE N is the number of elements in the data Example:The manager of a food chain recorded the number of customers who came to eat the products in each day.The results were 10,15,14,13,20,19,12 and 11. In this example N=8

26. MENDENHALL AND SINCICH METHOD A METHOD OF FINDING THE QUARTILE VALUE 1. CALCULATE THE POSITION OF THE LOWER QUARTILE 4 Lower Quartile (L) = Position of Q1 = 1 ( n +1)

27. MENDENHALL AND SINCICH METHOD A METHOD OF FINDING THE QUARTILE VALUE 2. CALCULATE THE POSITION OF THE UPPER QUARTILE 4 Upper Quartile (U) = Position of Q3 = 3 ( n +1)

28. MENDENHALL AND SINCICH METHOD A M ET H O D O F F I N D I N G T H E Q U AR T I L E VAL U E 4 Position of Q1 = 1 ( n +1) = 1 ( 9 +1) 4 = 2.5 (round up) = 3 THE LOWER QUARTILE VALUE Q1 IS THE 3 RD DATA ELEMENT, SO Q1 = 5 4 1 ( n +1) and round off to the nearest integer. EXAMPLE DATA SET {1, 3, 5 7, 16, 21, 27, 30, 31} and n = 9 To find Q1 locate its position using the formula

29. MENDENHALL AND SINCICH METHOD A M ET H O D O F F I N D I N G T H E Q U AR T I L E VAL U E 4 Position of Q3 = 3 ( n +1) = 3 ( 9 +1) 4 = 7.5 (round down) = 7 THE UPPER QUARTILE VALUE Q3 IS THE 7 TH DATA ELEMENT, SO Q3 = 27 4 3 ( n +1) and round off to the nearest integer. EXAMPLE DATA SET {1, 3, 5, 7, 16, 21, 27 , 30, 31} and n = 9 To find Q3 locate its position using the formula

30. DECILES

31. PERCENTILES

32. M E A S U R E S O F P OS I T I O N with Computer Application