Question

"The average (mean) of 20 numbers is 30, and the average of 30 other numbers is 20. What is the average of all 50 numbers?" The harmonic mean seems to work on this 2/[(1/20)+(1/30)] = 24. Does the harmonic mean work properly with any sets of averages in the form of this question?

Answer 1

avg = sum of n numbers/ n

so the avg of all numbers = { (20 * 30) + (30 * 20) } / (20 + 30)

(600 + 600) / 50 = 1200/ 50 = 24..

Answer 2

I'm aware of the answer to the question; that's not what I am concerned with.

Answer 3

Thanks, though.

Answer 4

ohkeyy, i will try to explain you...

Answer 5

Harmonic Mean between two numbers x and y is given by:

\[\huge H.M. = \frac{2xy}{x+y}\]

Answer 6

@waterineyes There was a Maths Processing Error.

Answer 7

avg = sum of n numbers/ n ..

so in the 1st case ... 30 = (sum of numbers) / 20...
So sum of Numbers = 30 * 20 = 600...

Similarly for second part... 20 = (sum of numbers) / 30..
So sum of Numbers = 20 * 30 = 600..

Now the complete average, as per formula is = (600 + 600) / (20 + 30 ).. (sum / total number)

1200/ 50 = 240..

understood ??

Answer 8

I think the answer would be 24 @Ganpat

Answer 9

@Ganpat I understand. I have understood that method when I asked this question. My question is specifically about if the harmonic mean can always be applied to questions of this type.

Answer 10

@waterineyes : oh sorry, its 24.. yes of course.. u understand the logic behind this.. and this can be applied to all the related questions.. with little change in data in regard with question..
what say @waterineyes ??

Answer 11

For verification, we apply the same question to other situation..

Let the average age of 15 students is 30 and average age of 20 students is 80,

For this Harmonic Mean According to the question will be:

2/(7/60) = 120/7

Now find the Arithmetic Mean = (15*30 + 20*80)/35 = 410/7

So, I think you can apply this Logic to this question only...

In General, you cannot use this Logic..

Answer 12

Thank you.

Answer 13

Welcome dear..