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?

- anonymous

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- anonymous

here geometric mean will be used...

- anonymous

\[(1.2)(1.3)(1.45) = 2.262\] so increase is 162.2%

- anonymous

divide by 3 and get average increase i guess

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## More answers

- anonymous

well satellite u have not been able to help me

- anonymous

oh sorry

- anonymous

use the formula sigma logx/n

- anonymous

and then take the antilog

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

ya.........

- anonymous

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

- anonymous

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

- 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%

- anonymous

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

- anonymous

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

- anonymous

why did u not take 1.312

- Hero

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

- anonymous

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

- anonymous

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

- anonymous

ok ,satellite why didnt we just use the mean?

- anonymous

gotta run, see you later

- anonymous

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

- anonymous

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

- anonymous

i have a similar ques

- Hero

tanusingh, have you considered khan academy or patrick JMT?

- anonymous

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

- Hero

http://patrickjmt.com
Try that..

- Hero

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

- anonymous

lets try hero

- anonymous

satellite is very gud in maths but he also got stuck

- anonymous

nah no help

- 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.

- anonymous

herosorry but u r also goood

- Hero

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

- anonymous

ah s.c gupta (indian author

- Hero

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

- anonymous

statistcal methods by s.c gupta

- Hero

I'll try to find it

- Hero

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

- anonymous

thanks anyway

- Hero

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

- Hero

Okay, I'll try to help you but I must ask, "What is your issue with Satellite's solution?".

- anonymous

why isnt mean used?

- anonymous

his ans is mathematically right

- Hero

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

- Hero

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

- anonymous

i knw.....

- anonymous

it is a g.m formula for ungrouped data

- Hero

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

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