## anonymous 4 years ago the population of a country increased in first decade by 20%,30% in the second decade and 45% in the third decade.what is the average rate of increase/decade in the population?

1. anonymous

here geometric mean will be used...

2. anonymous

$(1.2)(1.3)(1.45) = 2.262$ so increase is 162.2%

3. anonymous

divide by 3 and get average increase i guess

4. anonymous

well satellite u have not been able to help me

5. anonymous

oh sorry

6. anonymous

use the formula sigma logx/n

7. anonymous

and then take the antilog

8. anonymous

if you want the geometric mean it will $\sqrt[3]{1.2\times 1.3\times 1.45}$

9. anonymous

hey no this is an alternate formula of g.m in statistics is sigma logx/n

10. anonymous

you want $\frac{ln(1.2)+\ln(1.3)+\ln(1.45)}{3}$?

11. anonymous

ya.........

12. anonymous

and what is d logic of using g.m here and not d mean?

13. anonymous

in the book they have also use the compound interst formula alternatively

14. anonymous

http://www.wolframalpha.com/input/?i=e%5E%28%28ln%281.2%29%2Bln%281.3%29%2Bln%281.45%29%29%2F3%29 so i guess average is 31.27%

15. anonymous

ya.......and the wolfram thing is beyond my maths level

16. anonymous

i just plugged in the numbers to the formula you provided. you should be able to see exactly what i typed in

17. anonymous

why did u not take 1.312

18. Hero

How come you just can't do : (20 + 30 + 45)/3 = 31.6667% average increase?

19. anonymous

because this is the total after the increase. the increase itself is what comes after the one in the decimal

20. anonymous

for example if i want to increase a number by 30% i multiply it by 1.3

21. anonymous

ok ,satellite why didnt we just use the mean?

22. anonymous

gotta run, see you later

23. anonymous

i don't know, you said the book said to use the formula you provided

24. anonymous

bye....i think becoz the population grows exponetially

25. anonymous

i have a similar ques

26. Hero

tanusingh, have you considered khan academy or patrick JMT?

27. anonymous

ya.......khan academy......but not for dis ques

28. Hero

http://patrickjmt.com Try that..

29. Hero

Well, looks like Patrick doesn't have much for Prob and Stats

30. anonymous

lets try hero

31. anonymous

satellite is very gud in maths but he also got stuck

32. anonymous

nah no help

33. Hero

lol, I am in no position to help you. If Sat can't do it, I don't know who can. He's the smartest guy on here besides James. Now, that's someone you should probably consult.

34. anonymous

herosorry but u r also goood

35. Hero

I don't even have a stats book. I could probably find one though. Which one are you using?

36. anonymous

ah s.c gupta (indian author

37. Hero

I don't think I would be able to find that book. I think the solution satellite provided is accurate though.

38. anonymous

statistcal methods by s.c gupta

39. Hero

I'll try to find it

40. Hero

There doesn't seem to exist an online version of the book.

41. anonymous

thanks anyway

42. Hero

I hope you find the help you're looking for. Have you consulted James yet?

43. Hero

44. anonymous

why isnt mean used?

45. anonymous

his ans is mathematically right

46. Hero

He followed the formula you gave him. That's all that's required. I don't believe geometric mean applies to the formula.

47. Hero

You said it yourself, the formula is an alternative to the geometric mean formula.

48. anonymous

i knw.....

49. anonymous

it is a g.m formula for ungrouped data

50. Hero

What exactly is it about it that you don't understand? It's just a formula. You plug the numbers in and solve.