The average marks taken by both Male and Female students over a period of ten years under study is 52. The average marks of Female students in 10 years have never been below 50. But for Male students the average marks fluctuated below and above 50 in the 10 years. That explains the deviation. The standard deviation in 10 years data is 16 for Male students and 14 for Female students. The range of marks taken by Male students is between 0 and 100 and by Female students is between 11 and 98 in ten years. This is consistent with standard deviation. This is evident from table and chart in the appendix 2
And standard deviations of marks taken in different years say the Female students scored similar marks in the initial 2 to 4 years period of the study and their marks started varying a lot in the later years. The standard deviation was 6, 9 and 11 during first four years of study and later the standard deviation was well above 11. For the male students the standard deviation is high from the beginning indicating the marks scored by Male students varied at large. For the year 2001, both Male and Female students have similar and high standard deviation above 16. This is evident from table and chart in the appendix 2
The correlation coefficient is negative (-0.69) in case of enrollment of male and female students meaning the number of students enroll is inversely related between male and female students. ...
The correlation coefficient is a measure of nature and strength of relationship. This can be used to measure the nature and strength of relationship that Male students and Female students share.
The correlation coefficient is negative (-0.69) in case of enrollment of male and female students meaning the number of students enroll is inversely related between male and female students. The more the number of male students, the less the number of female students enrolled for the course in the past.
But, the marks correlation and coefficient is positive (0.55) meaning both male and female students marks are positively related. The scores travel in same direction for both male and female students. This is evident from charts in the appendix 3.
For any probability distribution & any value of h>0 we choose
For example, set h=2, then Tchebycheff's Inequality gives
Tested the above inequality with the scores data provided for 10 years for both male and female separately.
The marks scored by Male students and Female Students are considered and the scores outside average and 2 standard deviations are identified and their proportions are well less than 0.25. The is evident from tables in Appendix4
The analysis of the outcome is higher proportion of females students have outlier values as compared to Male students. The same can be tested for different sigma levels.
The Bayes' rule is used to find the probability of a gender given a student with more than or equal to 75% marks is chosen. i.e., A student with more than or equal to 75% marks has been chosen and the probability that student is male or female is found with the help of Bayes' rule.
P(A) = P(Male scoring at least 75%)
P(B) = P(Female