5.3-Measures-of-Central-Tendency-Grouped.pptx

Statistics and Probability:
Measures of central tendency;
Mode, median, mean, range

1. MEASURES OF CENTRAL TENDENCY (Grouped Data)

2.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 CLASSES CLASS LIMITS TALLY f 2 8 5 11 2                    

3.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 Classmarks fx Class Boundaries CLASSES f Less than Cumulative Frequency (< cf ) Midpoint x Class Limits    

4.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f Cumulative Frequency       14       19 24 29 34 39          

5.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f Cumulative Frequency 14       19 24 29 34 39 98     38     192 145 374 78    

6.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f Cumulative Frequency 14 19 24 29 34 39 98 38 192 145 374 78        

7.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f Cumulative Frequency 14 19 24 29 34 39 98 38 192 145 374 78 lower boundary lower class - - - - - - lower boundary upper boundary - 0.5 upper boundary upper class + 0.5         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5

8.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f Cumulative Frequency 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35

9.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35

10.   MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mean              

11.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35

12.   MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mean                

13.   MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median                  

14. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median          

15.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35

16. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median for Grouped Data 1. Locate the Median Class 2. Use the cumulative frequency that is lower than the median class. Divide n by 2 then locate the result in the cumulative frequency.

17. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median for Grouped Data 3. Use the values of the lower boundary & frequency of the median class.

18.         MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median

19.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35  

20.           MEASURES OF CENTRAL TENDENCY-GROUPED DATA Median

21. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode                  

22. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode      

23. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode for Grouped Data 1. Locate the Modal Class 2. Use the lower boundary of the modal class The class with the highest frequency

24. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode for Grouped Data 3. Find d 1 Difference between the frequency of the modal class and the frequency preceding it.

25. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode for Grouped Data 4. Find d 2 Difference between the frequency of the modal class and the frequency succeeding it.

26.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35

27.             7 12 - 16 17 22 27 32 37 - 21 - 26 - 31 - 36 - 41 2 8 5 11 2 x fx Class Boundaries CLASSES f 14 19 24 29 34 39 98 38 192 145 374 78 - - - - - -         11.5 16.5 21.5 26.5 31.5 36.5 16.5 21.5 26.5 31.5 36.5 41.5 cf 7 9 17 22 33 35              

28. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Mode      

29. MEASURES OF CENTRAL TENDENCY-GROUPED DATA Measures of Central Tendency       Mode Median Mean

30. The data shown represent the number of kilometer per gallon that 42 selected four-wheel-drive sports utility vehicles obtained in city driving. Construct a frequency distribution with 10 classes. FREQUENCY DISTRIBUTION – Take Home Exercise 46 48 64 76 78 54 39 76 94 61 80 48 60 64 59 62 57 65 86 69 57 61 58 93 72 64 57 66 41 67 59 65 90 56 71 72 75 27 68 61 94 86 41 68 59 61 69 68 59

31. 46 48 64 76 78 54 39 80 48 60 64 59 62 57 57 61 58 93 72 64 57 59 65 90 56 71 72 75 94 86 41 68 59 61 69 76 65 66 27 68 67 61

32. CLASSES Tally f                     27 - 33 34 41 48 55 62 - 40 - 47 - 54 - 61 - 68 69 76 83 90 75 82 89 96 - - - - 1 1 2 3 12 10 5 4 1 3