Group-2-Measure-of-Kurtosis-1.pptx

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1. Measure of Kurtosis Presented by: Group 2

2. Objectives: Discuss what Kurtosis is. Compute the Kurtosis for both the grouped and ungrouped data. Be able to describe the Kurtosis measurement.

3. 1 st type Leptokurtic Kurtosis - refers to the degree to which a distribution is peaked or flat. 3 types of Kurtosis 2 nd type 3 rd type Mesokurtic Platykurtic It has less kurtosis than the normal distribution . The kurtosis of this distribution is comparable to that of the normal distribution. It has more kurtosis than the normal distribution. K < 3 K = 3 K > 3

4. 3 types of Kurtosis

5. Formulas used in Ungrouped data of Kurtosis

6.   Where: Xi = Individual Values = Mean n = Number of Observations s = Standard Deviation   Mean: For Ungrouped Data:     Standard Deviation:

7. Solve this!

8. U ngrouped Kurtosis Xi 6 7 9 11 13 15 16 Σ = 77        

9. U ngrouped Kurtosis - ( - 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625 S   S   S   S   S   v v

10. U ngrouped Kurtosis - ( - 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625 S   S   S   S   S  

11. U ngrouped Kurtosis - ( - 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625 6 6 - 11 - 5 25 625 7 7 - 11 - 4 16 256 9 9 - 11 - 2 4 16 11 11 - 11 13 13 - 11 2 4 16 15 15 - 11 4 16 256 16 16 - 11 5 25 625           Since K-computed 1.14 is < 3, therefore the distribution is Platykurtic .

12. Formulas used in Grouped data of Kurtosis

13. For Grouped Data: Mean : Standard Deviation:       Where: Xi = Class Mark = Mean n = Number of Observations s = Standard Deviation  

14. Grouped Kurtosis C.I Frequency Xi FiXi 76 - 79 2 77.5 155 80 – 83 5 81.5 407.5 84 - 87 5 85.5 427.5 88 - 91 11 89.5 984.5 92 - 95 4 93.5 374 96 - 99 3 97.5 292.5 n = 30 Σ = 2,641 |Xi – X| 10.53 6.53 2.53 1.47 5.47 9.47       vv

15. Grouped Kurtosis C.I Frequency Xi FiXi 76 - 79 2 77.5 155 80 – 83 5 81.5 407.5 84 - 87 5 85.5 427.5 88 - 91 11 89.5 984.5 92 - 95 4 93.5 374 96 - 99 3 97.5 292.5 n = 30 Σ = 2,641 |Xi – X| 10.53 6.53 2.53 1.47 5.47 9.47      

16. C.I Frequency Xi FiXi |Xi – X| Fi |Xi – X| Fi |Xi - X |² Fi|Xi - X|⁴ 76 - 79 2 77.5 155 10.53 21.06 221.7618 24,589.1480 80 – 83 5 81.5 407.5 6.53 32.65 213.2045 9,091.2318 84 - 87 5 85.5 427.5 2.53 12.65 32.0045 204.8576 88 - 91 11 89.5 984.5 1.47 16.17 23.7699 51.3644 92 - 95 4 93.5 374 5.47 21.88 119.6836 3,581.041 96 - 99 3 97.5 292.5 9.47 28.41 269.0427 24,127.9915 n = 30 Σ = 2,641 Σ = 132.82 Σ = 879.467 Σ = 61,645.6343 Grouped Kurtosis v v vv

17. Grouped Kurtosis C.I Frequency Xi FiXi |Xi – X| Fi |Xi – X| Fi |Xi - X |² Fi|Xi - X|⁴ 76 - 79 2 77.5 155 10.53 21.06 221.7618 24,589.1480 80 – 83 5 81.5 407.5 6.53 32.65 213.2045 9,091.2318 84 - 87 5 85.5 427.5 2.53 12.65 32.0045 204.8576 88 - 91 11 89.5 984.5 1.47 16.17 23.7699 51.3644 92 - 95 4 93.5 374 5.47 21.88 119.6836 3,581.041 96 - 99 3 97.5 292.5 9.47 28.41 269.0427 24,127.9915 n = 30 Σ = 2,641 Σ = 132.82 Σ = 879.467 Σ = 61,645.6343

18. Grouped Kurtosis          

19. Grouped Kurtosis           Since K-computed 2.23 is < 3, therefore the distribution is Platykurtic .

20. Thank you! Presented by: Group 2