MHB How do I find the average of two averages?

[Math_312 46]

In a statistical study, several measurements were taken and the average value of the measurements was 10.2. In a new survey, twice as many measurements were taken and the mean of these measurements was 10.8. What is the mean of all the measurements?

 

[HOI]

If the mean of "n" numbers is is 10.2 what is their sum?
If the mean of "2n" numbers is 10.8, what is their sum?

So what is the sum of all 3n items? What is theit mean?

 

[Math_312 46]

Are you suggesting that I do this:
10.2 n / n = 10.2

or have I misunderstood you?

 

[skeeter]

$\dfrac{10.2 \cdot n + 10.8 \cdot 2n}{n + 2n}$

 

[Math_312 46]

$\dfrac{10.2 \cdot n + 10.8 \cdot 2n}{n + 2n}$

So if I do this calculation, the answer is 21?

 

[skeeter]

So if I do this calculation, the answer is 21?

no

 

[Math_312 46]

no

Is it then 7 or 15,9?

 

[skeeter]

Is it then 7 or 15,9?

nosimplify the numerator
what does $(10.2)(n) + (10.8)(2n)$ equal?

simplify the denominator
what does $n+2n$ equal?

determine those two sums, then divide.

 

[Math_312 46]

nosimplify the numerator
what does $(10.2)(n) + (10.8)(2n)$ equal?

simplify the denominator
what does $n+2n$ equal?

determine those two sums, then divide.

Ah, I see now. So the answer is then 10,6?

 

[HOI]

Are you suggesting that I do this:
10.2 n / n = 10.2

or have I misunderstood you?

I was suggesting that you ANSWER THE QUESTIONS I ASKED!

 

[HOI]

I said, in my first response was

If the mean of "n" numbers is is 10.2 what is their sum?

10.1n

If the mean of "2n" numbers is 10.8, what is their sum?

(10.8)(2n)= 21.6n

So what is the sum of all 3n items?[\quote]
10.1n+ 21.6n= 31.7n

What is their mean?

31.7n/(3n)= 31.7/3= 10.5666...

 

[Kansas Boy]

You have the wrong answer because n times 10.2 is 10.2n NOT 10.1n as you used.
2n times 10.8 is 21.6n as you have.

Altogether those add to 10.2n+ 21.6n= 31.8n.

The average of those 3n values is 31.8/3= 10.6.