DOC-20240424-WA0005. new.pptx statistics

Statistics

1. Paper 3:Assessment for learning Module 5: Statistics TOPIC : SD – shortcut method, Computation of correlation coefficient

2. Let’s Remember What is Standard deviation? SD is the square root of the arithmetic average of the squares of the deviation measured from the mean.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean.

3. It is a popular measure of variability.
It is the most widely used measure of dispersion, is based on all values. a change in even one value affects the value of standard deviation. It is also useful in certain advanced statistical problems.

4. For ungrouped data

5. For grouped data where f = frequency X = mid value of class interval M = Arithmetic mean N = total frequency

6. Shortcut method/ Assumed mean method i = class width / class interval f = frequency N = total frequency d = deviation of midpoint from assumed mean in terms of class interval

7. Calculate SD in shortcut method CI 45 - 49 40 - 44 35 - 39 30 - 34 25 - 29 20 - 24 15 - 19 10- 14 5 - 9 f 2 3 2 5 9 8 7 7 7

8. Ans . CI f Mid X d = (X-A)/ i fd d^2 f × d^2 45-49 2 47 4 8 16 32 40-44 3 42 3 9 9 27 35-39 2 37 2 4 4 8 30-34 5 32 1 5 1 5 25-29 9 27 20-24 8 22 -1 -8 1 8 15-19 7 17 -2 -14 4 28 10-14 7 12 -3 -21 9 63 5-9 7 7 -4 -28 16 112 N=50 Σ fd = -45 Σ(f × d^2) = 283

9. Calculate SD in shortcut method CLASS INTERVAL FREQUENCY 127-129 1 124-126 2 121-123 3 118-120 1 115-117 6 112-114 4 109-111 3 106-108 2 103-105 1 100-102 1

10. CORRELATION Correlation refers to a process for establishing the relationships between two variables.

11. Coefficient of correlation The ratio indicating the degree of correlation is known by the term coefficient of correlation It is used to measure the intensity of the relation It involves no unit and varies from -1 to +1

12. The range of computed correlation coefficient Interpretation Absolutely no relationship From 0 to ± 0.2 All most negligible relationship From ± 0.21 to ± 0.4 Low correlation From± 0.41 to ± 0.7 Moderate correlation From ± 0.71 to ± 0.9 High correlation From ± 0.91 to ± 0.99 Very high correlation ± 1 Perfect correlation

13. Computation of correlation coefficient There are two methods for calculating coefficient of correlation Karl Pearson’s product moment method Spearman’s rank difference method

14. 1.Karl Pearson’s product moment method N is the number X and Y are two sets of score

15. Calculate coefficient of correlation using product moment method or Pearson’s method Subject Scores in test X Scores in test Y A 5 12 B 3 15 C 2 11 D 8 10 E 6 18

16. Ans . Subject Scores in test X Scores in test Y X^2 Y^2 XY A 5 12 25 144 60 B 3 15 9 225 45 C 2 11 4 121 22 D 8 10 64 100 80 E 6 18 36 324 108 ΣX = 24 ΣY = 66 Σ X^2 = 138 Σ Y^2 = 914 ΣXY= 315

17. Interpretation : There is a negligible negative correlation between scores in test X and scores in test Y

18. 2. Spearman’s rank difference method D is the difference in ranks N is the number

19. Calculate coefficient of correlation using rank difference method Subject Scores in test X Scores in test Y A 8 4 B 7 7 C 9 6 D 5 8 E 1 10

20. Ans . Subject Scores in test X Scores in test Y R1 R2 D =R1-R2 D^2 A 8 4 2 5 -3 9 B 7 7 3 3 C 9 6 1 4 -3 9 D 5 8 4 2 2 4 E 1 10 5 1 4 16 Σ D^2 =38

21. Interpretation : there is a high negative correlation between the variables

22. Calculate the coefficient of correlation using rank difference method Students Scores in test X Scores in test Y A 12 21 B 15 25 C 24 35 D 20 24 E 8 16 F 15 18 G 20 25 H 20 16 I 11 16 J 26 38

23. Ans . Students Scores in test X Scores in test Y R1 R2 D = R1-R2 D^2 A 12 21 8 6 2 4 B 15 25 6.5 3.5 3 9 C 24 35 2 2 D 20 24 4 5 -1 1 E 8 16 10 9 1 1 F 15 18 6.5 7 -0.5 0.25 G 20 25 4 3.5 0.5 0.25 H 20 16 4 9 -5 25 I 11 16 9 9 J 26 38 1 1 Σ D^2 = 40.5

24. Interpretation : there is a high positive correlation between the variables

25. Review Questions What is SD? What is the shortcut method to find SD? What are the methods to compute coefficient of correlation?

26. THANK YOU