Question

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?

Answer 1

here geometric mean will be used...

Answer 2

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

Answer 3

divide by 3 and get average increase i guess

Answer 4

well satellite u have not been able to help me

Answer 5

oh sorry

Answer 6

use the formula sigma logx/n

Answer 7

and then take the antilog

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

ya.........

Answer 12

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

Answer 13

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

Answer 14

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%

Answer 15

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

Answer 16

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

Answer 17

why did u not take 1.312

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

ok ,satellite why didnt we just use the mean?

Answer 22

gotta run, see you later

Answer 23

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

Answer 24

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

Answer 25

i have a similar ques

Answer 26

tanusingh, have you considered khan academy or patrick JMT?

Answer 27

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

Answer 28

http://patrickjmt.com

Try that..

Answer 29

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

Answer 30

lets try hero

Answer 31

satellite is very gud in maths but he also got stuck

Answer 32

nah no help

Answer 33

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.

Answer 34

herosorry but u r also goood

Answer 35

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

Answer 36

ah s.c gupta (indian author

Answer 37

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

Answer 38

statistcal methods by s.c gupta

Answer 39

I'll try to find it

Answer 40

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

Answer 41

thanks anyway

Answer 42

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

Answer 43

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

Answer 44

why isnt mean used?

Answer 45

his ans is mathematically right

Answer 46

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

Answer 47

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

Answer 48

i knw.....

Answer 49

it is a g.m formula for ungrouped data

Answer 50

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