A brief sketch of Shri Madhvacharya by Dr. Prhabanjanacharya Shri Madvacharya is Thrilokaachaya. He showed the way to liberation (or salvation). He acquired entire knowledge of shaastras. He is responsible for guiding multiple crores of Saatvik people. He analyzed Vedavyasa’s Brahma Sutra. “Sumadvha Vijaya” written by Shri Narayana Pandithacharya contains 1008 shlokas which depicts the entire memoirs of Acharya. Acharya’s childhood is similar to that of lord Krishna. When Acharya as an infant consumed horse gram no side effects could be seen on the child. By offering tamarind seeds to his father’s friend he solved the loan problem of his father. When he was just one year old, he went around the place by holding the tail of a bull. He had consumed 200/1000 plantains at different times without any effect to the stomach. He drank milk from 30 big vessels (khodas). He cured the head ache of his teacher’s son by blowing air into his ear. From “Sumadhva Vijaya”, we learn that how Acharya taught the world how to respect parents. When Acharya wanted to take up Sanyasa, his parents requested him not to take up Sanyasa as he was the only son surviving and there would be nobody to look after them in their old age. Acharya consented and promised that he would not take Sanyasa till his parents had another male child. He took to Sanyasa only after the birth of his younger brother Vishnu Theertha. When Acharya went to see Vedavyasa to Dodda Badari, his disciple Sathya Thirtha could not keep pace with Acharya and he was forced to come back to Chikka Badari which is the place often visited by us now. Acharya proved that he was the incarnation of Hanuman. Acharya did mouna vrutha (silent vow) for 48 days in Badari and he bathed in the Alakananda river daily during the dawn time. He used to bathe thrice a day in the Alakananda river. Once when thieves tried to rob him, he made them fight among themselves and foiled their attempt. When a giant in the form of a tiger jumped at his disciple Sathya Theertha, he killed the tiger merely by touching it by hand. This is an illustration to show how Acharya saves those who do upasane of GOD. Acharya protects all those who read or understand Brahma Sutra from danger. Acharya could cross the Ganga river easily with his disciples. Acharya responds in the same language of the King. When the King questions Acharya how he could cross the Ganga River where he had kept his guards everywhere. Acharya said him he could perform this feat with the help of Lord (GOD) who is surrounded by the Sun. The king offered him half of his kingdom. The doors of Vaikunta are open to those who are perfect in both loukika vidye and shaasthra vidye. To understand Madhva shaastra, one should become a student of Madhva philosophy. Initiation towards Madhva shaastra is essential to understand Madhva shaastra. Achaya spread the navavidha bhakthi in the universe. 'I acknowledge with gratitude the services of Shree K.K. Raghavendra Rao of the Indian Railways, (retired), who went through the article and gave valuable suggestions Prepared by: - J. Sudhindra Simha, Bengaluru

interpolation

Dear Friends,

This is just an introduction letter.My name is J. Sudhindra Simha. My qualification is M.Sc. in Statistics from the University of Mysore, Karnataka, India. I have also obtained Certificate in Population Studies, IIPS, Mubai. I am retired now.
I have about 9-10 published papers in family planning methods while I was working for the Christian Medical Association of India, Bangalore.
I have also worked as Lecturer for BBM course in Bangalore. I have developed some simple modules in the application of statistics and demography in different topics which may be helpful to under graduate students and professional courses also. Hence, I would like to share this with interested groups who would benefit from this. As I have opened a blog, I want to display it.

The topics covered are :-

1. Interpolation
2. Central Tendency
3. Dispersion
4. Regression analysis
5. Probability
6. Testing of Hypothesis
7. Life expectancy
8. Age at marriage.

As a first step I am attaching herewith “Interpolation”.

Regards,
J. Sudhindra Simha

9/25/2009

Find a suitable method of interpolation to find the value of y when x=7?


















x 2 4 6 8







y 7 21 43 73







x y ∆ ∆2 ∆3







2 7












14

use newton's backward





4 21
8
formula








22
0

y n 73



6 43
8


vΔy n-1 -15





30

+{ v(v+1)/1.2} Δ2y n-2 -1



8 73





57



x=7 xn=8 v=(x-xn)/h v=(7-8)/2 v=-0.5







h=2


h
















Applying Newton’s Backward Interpolation formula we get
































y7 = 73 -15 -1 57








y7 = 57






















































































x y ∆ ∆2 ∆3






















0

use newton's backward


-1




0
formula








0
0

y n= 0






0


vΔy n-1= #DIV/0!





0

+{ v(v+1)/1.2} Δ2y n-2= #DIV/0!










= #DIV/0!



x=
xn=









h=
v= (x-xn)/v










v= #DIV/0!








Applying Newton’s Backward Interpolation formula we get
































y7 = #DIV/0!
























Using Newton's method of interpolation find from the data given below, the number of




the number of persons in the income group between Rs.20 and Rs.25?

Wages No. of










(inRs.) persons ∆ ∆2 ∆3 ∆4






Below10 20












25









Below20 45
45










70
-20







Below30 115
25
15








95
-5







Below40 210
20










115









Below 50 325























h= 10 x= 20 x0= 10 u=(x-x0)/h= 1





10 x= 25 x0= 10 u=(x-x0)/h= 1.5



u= 1.5 (u/1)∆Y0= 37.5










(u)(u-1)/(1*2)*(∆2y0)= 16.88









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= 1.25








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)= 0.35



















u= 1 (u/1)∆Y0= 25
y0 = 20







(u)(u-1)/(1*2)*(∆2y0)= 0









Applying Newton’s forward interpolation formula, we get






Y = y0 + (u/1) Dy0 + {u(u-1)/1.2}D2y0 + {u(u-1)(u-2)/1.2.3}D3y0 + -------------



--------------+ {u(u-1)u-2)…………..(u-n+1)/1.2.3…..n}Dny0







y20 = 20 + 25 = 45



y25 = 20 + 37.5 + 16.88 + 1.25 + 0.35 = 75.98
















y25 - y20 = 30.98 = 31



Hence the number of persons in the income group between Rs.25 and Rs.20 are 31.






























DATA: First two columns are given






















To estimate the candidates getting more than 48 marks and less than 50 marks. rks but not more than 50 marks.



























Marks No. of










upto candidates ∆ ∆2 ∆3 ∆4






45 447












37









50 484
-16










21
1







55 505
-15
11








6
12







60 511
-3










3









65 514


















z



h= 5 x= 50 x0= 45 u=(x-x0)/h= 1




h= 5 x= 48 x0= 45 u=(x-x0)/h= 0.6




0.6 (u/1)∆Y0= 22.2










(u)(u-1)/(1*2)*(∆2y0)= 1.92









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= 0.056








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)= -0.37




















1 (u/1)∆Y0= 37
y0 = 447







(u)(u-1)/(1*2)*(∆2y0)= 0









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= 0








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)=
0







Applying Newton’s forward interpolation formula, we get






Y = y0 + (u/1) Dy0 + {u(u-1)/1.2}D2y0 + {u(u-1)(u-2)/1.2.3}D3y0 + -------------



--------------+ {u(u-1)u-2)…………..(u-n+1)/1.2.3…..n}Dny0







y48= 447 + 22.2 = 469



y50= 447 + 37 + 0.00 + 0.00 + 0.00 = 484.00
















y50 - y48 = 14.80 = 13




The number of candidates who get more than 48 marks but not more than 50 marks are 13.


The number of candidates who get more than
marks but not more than



marks are













































































∆ ∆2 ∆3 ∆4





















0












0










0
0










0
0








0
0










0










0



































h=
x= 0 x0= 10 u=(x-x0)/h= #DIV/0!






x=
x0= 10 u=(x-x0)/h= #DIV/0!




#DIV/0! (u/1)∆Y0= #DIV/0!










(u)(u-1)/(1*2)*(∆2y0)= #DIV/0!









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= #DIV/0!








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)= #DIV/0!




















#DIV/0! (u/1)∆Y0= #DIV/0!
y0 = 20







(u)(u-1)/(1*2)*(∆2y0)= 0









Applying Newton’s forward interpolation formula, we get






Y = y0 + (u/1) Dy0 + {u(u-1)/1.2}D2y0 + {u(u-1)(u-2)/1.2.3}D3y0 + -------------



--------------+ {u(u-1)u-2)…………..(u-n+1)/1.2.3…..n}Dny0







y20 = 20 + #### = ####




20 + #DIV/0! + #DIV/0! + #DIV/0! + #DIV/0! = #DIV/0!
















y25 - y20 = #DIV/0! =

















Hence the number of persons in the income group between Rs.
and Rs.


are











DATA: First two columns are given






















To estimate the candidates getting more than 48 marks and less than 50 marks. rks but not more than 50 marks.




























Marks No. of










upto candidates ∆ ∆2 ∆3 ∆4





















0












0










0
0










0
0








0
0










0










0






























z



h=
x=
x0= 0 u=(x-x0)/h= #DIV/0!




h=
x=
x0= 0 u=(x-x0)/h= #DIV/0!




#DIV/0! (u/1)∆Y0= #DIV/0!










(u)(u-1)/(1*2)*(∆2y0)= #DIV/0!









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= #DIV/0!








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)= #DIV/0!




















#DIV/0! (u/1)∆Y0= #DIV/0!
y0 = 0







(u)(u-1)/(1*2)*(∆2y0)= #DIV/0!









(u)(u-1)(u-2)/(1*2*3)*(∆3y0)= #DIV/0!








(u)(u-1)(u-2)(u-3)/(1*2*3*4)*(∆4y0)=
#DIV/0!







Applying Newton’s forward interpolation formula, we get






Y = y0 + (u/1) Dy0 + {u(u-1)/1.2}D2y0 + {u(u-1)(u-2)/1.2.3}D3y0 + -------------



--------------+ {u(u-1)u-2)…………..(u-n+1)/1.2.3…..n}Dny0




y50= 0 + #DIV/0! + #DIV/0! + #DIV/0! + #DIV/0! = #DIV/0!
y48= 0 + #DIV/0! + #DIV/0! + #DIV/0! + #DIV/0! = #DIV/0!
















y50 - y48 = #DIV/0! = 13

















The number of candidates who get more than .
marks but not more than




marks are



































.